The Israeli military said on Thursday it had killed Muhammad Deif, the Hamas commander who is believed to have been a planner of the Oct. 7 attack on Israel, in an airstrike last month, which would make him the third Iranian-backed militant leader slain in recent weeks.

The Israeli announcement confirming the death of Mr. Deif, the leader of Hamas’s military wing, came as thousands of mourners attended the funerals of another Hamas leader and a Hezbollah commander whose assassinations this week have amplified fears of a wider regional war.

Mr. Deif was killed in an Israeli airstrike on a compound in southern Gaza on July 13, according to the Israeli military. It said his death had been confirmed by an intelligence assessment, but did not provide further details. At least 90 other people were killed in the strike, according to Gaza’s health officials.

Hamas has not confirmed or denied Mr. Deif’s death. The No. 2 Hamas leader in Gaza, he would be the group’s most senior military leader slain by Israeli forces during the offensive in Gaza that has also killed more than 38,000 people, according to the territory’s health officials. Israel began its campaign in the enclave after a Hamas-led attack on southern Israel on Oct. 7, during which 1,200 people were killed and about 250 abducted to Gaza.

Israeli leaders, who have said they will continue fighting in Gaza until they destroy Hamas’s military and governing capabilities, celebrated the announcement of Mr. Deif’s death, the latest revelation in a dizzying two days that have shaken the leadership of Hamas and Hezbollah, both of which are backed by Iran.

“Deif was responsible for the terrible massacre of Oct. 7 and for many murderous attacks against Israeli civilians,” Prime Minister Benjamin Netanyahu of Israel said in a statement. “He was Israel’s most-wanted person for years. His elimination establishes a very clear principle — whoever harms us, we will retaliate against them.”

The announcement came as large public funeral processions were held in Iran’s capital, Tehran, for Hamas’s political leader, Ismail Haniyeh, who was killed on Wednesday by an explosion in Tehran; and near Lebanon’s capital, Beirut, for a Hezbollah commander, Fuad Shukr, who was killed by an Israeli airstrike on Tuesday.

Israel has not admitted to killing Mr. Haniyeh, but American officials have assessed that it was responsible for the attack. Iran and Hamas blamed Israel, and Iran’s supreme leader, Ayatollah Ali Khamenei, ordered a direct strike on Israel in retaliation, according to three Iranian officials briefed on the order.

The killings of Mr. Shukr and Mr. Haniyeh have threatened to engulf the Middle East in a wider war and to derail cease-fire talks aimed at stopping the fighting in Gaza and releasing the remaining hostages there.

As the region braced for a possible escalation, some major airlines suspended flights to Tel Aviv and Beirut, and some of the families of the hostages protested outside Israeli military headquarters in Tel Aviv, expressing concern that a cease-fire deal was slipping away.

“Prime minister, there’s a deal on the table — a deal that you proposed,” Ella Ben-Ami, whose father, Ohad, remains held captive by Hamas, said at a rally in Tel Aviv. “Please, don’t sabotage it. Don’t break this deal. Bring them home.”

Secretary of State Antony J. Blinken, during a stop in Mongolia on Thursday, did not directly address a reporter’s question about whether Mr. Netanyahu had misrepresented his desire to negotiate a cease-fire in Gaza, given the escalating tensions in the Middle East caused by the assassinations.

“The path that the region is on is toward more conflict, more violence, more suffering, more insecurity,” Mr. Blinken said. “And it is crucial that we break the cycle, and that starts with a cease-fire. It’s urgent that all parties make the right choices in the days ahead.”

Mr. Haniyeh, who was a top negotiator in the cease-fire talks, was killed by a bomb planted and remotely detonated in the guesthouse in Tehran where he was staying after attending the inauguration of Iran’s new president.

Hours before Mr. Haniyeh was killed, Israeli fighter jets flew over Beirut’s southern suburbs and killed Mr. Shukr, a senior member of Hezbollah, the Lebanese militia that has been exchanging strikes with Israel for months in what it calls a show of solidarity with Hamas. Israel has said Mr. Shukr oversaw Hezbollah’s campaign against Israel, including a rocket attack that killed 12 children and teenagers in the Israeli-controlled Golan Heights last weekend.

On Thursday, throngs of mourners crowded the streets of Tehran for Mr. Haniyeh’s funeral procession, surrounding a canopied truck adorned with flowers and streamers and bearing his coffin. Many waved the flags of Iran, Palestine and Hezbollah.

Mr. Khamenei and Iran’s new president, Masoud Pezeshkian, wiped away tears during prayers for Mr. Haniyeh, video of the funeral showed. The ayatollah also hugged and greeted Mr. Haniyeh’s son, who was in Tehran for the funeral.

The commander of Iran’s armed forces, Gen. Mohammad Bagheri, also vowed to avenge the killing, saying at the funeral, “We are currently examining how we and the resistance will avenge the blood.” He added, “Different actions will take place that will make the Zionists regret it.”

At Mr. Shukr’s funeral inside a packed auditorium in Beirut’s southern suburbs, the crowd chanted, “Death to Israel,” and shouted, “We are here for you, Nasrallah,” as Hezbollah’s leader, Hassan Nasrallah, appeared on a video screen.

In his speech, Mr. Nasrallah said that Hezbollah would retaliate against Israel for the killing of Mr. Shukr. Hezbollah and its allies were working on “a true response, not a show response, as some are trying to suggest,” he said. His unusually brief remarks appeared to stop short of the full-throated pledge to escalate Hezbollah’s fight with Israel that some had been expecting.

“We have entered a new phase,” Mr. Nasrallah said. Addressing Israel, he said, “You do not realize the red lines you have crossed.”

Hezbollah has dialed back its attacks along Israel’s northern border since the killing of Mr. Shukr, and Mr. Nasrallah said in his speech that he had ordered his fighters to remain calm. But he said that the group would resume operations on Friday and that retaliation for Mr. Shukr’s death would come later.

After Mr. Nasrallah’s speech, Mr. Shukr’s coffin was carried to the street outside and met by a sea of mourners, pumping their fists in the air. “No escape, no retreat,” the crowd shouted.

Mr. Netanyahu said in his statement that the Israeli military was prepared for an attack.

“Israel is in very high readiness for any scenario — both defensively and offensively,” he said. “We will impose a very heavy price for any act of aggression against us from any front.”

Reporting was contributed by Lara Jakes, Qasim Nauman, Ephrat Livni, Hwaida Saad, Johnatan Reiss and Edward Wong.

A prisoner swap on Thursday among seven countries freed the Wall Street Journal reporter Evan Gershkovich and two other Americans held in Russia, along with several jailed Russian dissidents, in a deal whose size and complexity has no parallel in the post-Soviet era.

The trade freed 15 people imprisoned by Russia and one by its ally Belarus, in return for eight held in Western countries, including a convicted assassin and several held as Russian spies. It was all the more remarkable for taking place two and a half years into Russia’s invasion of Ukraine, which the Kremlin has cast as a war for Russian survival against the United States and its allies who are arming and financing Kyiv.

The deal, culminating a long and elaborate web of negotiations behind the scenes, delivered a diplomatic victory for President Biden, who has long pledged to bring home imprisoned Americans and to support Russia’s ruthlessly repressed democracy advocates, journalists and war critics.

“Their brutal ordeal is over, and they’re free,” Mr. Biden said at the White House, speaking of the freed Americans, whose relatives flanked him. “Moments ago, their families and I were able to speak to them on the phone from the Oval Office,” he said, and he wished them “welcome almost home.”

The exchange took place at the international airport in Ankara, Turkey’s capital, and involved seven planes ferrying the 24 prisoners from the United States, Germany, Poland, Slovenia, Norway and Russia, according to the Turkish government, which has positioned itself as a mediator between Moscow and the United States throughout the war in Ukraine.

It was a triumph of a different sort for President Vladimir V. Putin of Russia, who has long highlighted his loyalty to Russian agents captured abroad. In nearly a quarter-century in power, he has leveraged the Russian law enforcement and court systems for political advantage, using them as tools of domestic repression but also for the prosecution of foreigners, sometimes on sham espionage charges or drug offenses, for use in prisoner swaps.

The trade freed Mr. Gershkovich, 32, who had spent 16 months in a Russian prison; Alsu Kurmasheva, 47, a Russian American editor for Radio Free Europe/Radio Liberty who was also arrested last year; and Paul Whelan, 54, arrested in 2018. Five of those released were Germans or people with dual German and Russian nationality.

Secretary of State Antony J. Blinken, while traveling in Japan, told reporters that he had spoken with the Americans and that “they all sounded strong of voice, strong of mind, strong of spirit.” Officials said the three boarded a plane in Ankara bound for Joint Base Andrews near Washington, where Mr. Biden and Vice President Kamala Harris planned to meet them.

The deal also freed some of the best-known Russian critics of the Kremlin: Vladimir Kara-Murza, 42, a Washington Post contributor who won the Pulitzer Prize for commentary this year; Ilya Yashin, 41, a politician who spoke out against the war in Ukraine, an act Russia has criminalized; and Lilia Chanysheva, 42, and Ksenia V. Fadeyeva, 32, two associates of the opposition leader Aleksei A. Navalny, who died at 47 in a Russian prison in February.

Oleg Orlov, 71, the co-chairman of Memorial, the Russian human rights group, and Aleksandra Y. Skochilenko, 33, an artist who left price tags with antiwar messages in a supermarket, were also released.

In a statement, the Kremlin said that Mr. Putin had pardoned those convicted in Russia to enable their release, and that the country was “grateful to the leadership of all countries that assisted.”

In exchange, Germany released Vadim Krasikov, a Russian convicted of murdering a Chechen former separatist fighter in Berlin in 2019 on orders from the Russian government.

Slovenia set free Maria Mayer and Ludwig Gisch, whom the Slovenian authorities arrested in December 2022, accusing them of being Russian “illegals” — deep-cover spies — posing as Argentine immigrants and living in Ljubljana, the capital, under pseudonyms. On Wednesday, the two pleaded guilty to espionage and were sentenced by a Slovenian court.

The United States, Norway and Poland each released one person accused of spying for Russia, and the U.S. government also returned two Russian hackers convicted of financial cybercrimes.

Hours after the trade in Ankara, Mr. Putin greeted the Russians freed by the West on a red carpet laid out on the tarmac at the Vnukovo Airport in Moscow. State television showed him embracing Mr. Krasikov, the first off the plane, and clapping him on the back and upper arm.

“I want to congratulate all of you on your return to the motherland,” Mr. Putin told the group of returned Russians.

The deal was negotiated primarily by senior officials of the Central Intelligence Agency; its German counterpart, the B.N.D.; and the Federal Security Service, or F.S.B., the Russian domestic intelligence agency formerly known as the K.G.B.

The swap was the latest and largest of several prisoner exchanges that the Biden administration has negotiated with Mr. Putin even as the relationship between Russia and the United States has hit new lows over the war in Ukraine. In 2022, the United States freed Viktor Bout, a convicted Russian arms trafficker, in exchange for Russia’s release of Brittney Griner, the basketball star arrested on cannabis possession charges.

For Chancellor Olaf Scholz of Germany, agreeing to the release of Mr. Krasikov, the convicted assassin, was politically risky — a signal of his commitment to the alliance with the United States and to supporting the Russian opposition, but a gamble that voters would not punish his government for releasing the man convicted of one of the highest-profile killings in Germany’s recent history.

“I particularly owe a great sense of gratitude to the chancellor,” Mr. Biden said at the White House. “The demands they were making of me required me to get some significant concessions from Germany, which they originally concluded they could not do because of the person in question.”

The president took a swipe at Donald J. Trump, his predecessor, who has denigrated American allies and alliances. “For anyone who questions whether allies matter — they do, they matter,” Mr. Biden said. “And today is a powerful example of why it’s vital to have friends in this world.”

When a reporter asked about Mr. Trump’s claim that he could win the release of Americans from Russia without giving anything in return, Mr. Biden shot back, “Why didn’t he do it when he was president?”

The negotiations for a prisoner swap accelerated with the arrest of Mr. Gershkovich in March 2023 on espionage charges that were widely seen outside Russia as fabricated and denounced as fiction by his employer and the U.S. government.

Russian prosecutors accused the reporter of gathering classified information for the C.I.A. about a major military factory near Yekaterinburg, in the Ural Mountains. But they have not made public any evidence to back up the charge, and his trial was held behind closed doors.

Mr. Gershkovich, the American-born son of immigrants from the Soviet Union, became widely recognized in the West as a symbol of press freedom — or the lack of it — and of the threat to journalists in authoritarian countries. Before his arrest, he had lived and worked in Russia for six years, developing what friends described as a deep affection for the country’s people and culture.

The Wall Street Journal and journalist groups mounted a campaign throughout his incarceration to keep him in the public eye and maintain pressure for his release. In a joint statement on Wednesday, The Journal’s publisher, Almar Latour, and editor in chief, Emma Tucker, said, “We condemn in the strongest terms Vladimir Putin’s regime in Russia, which orchestrated Evan’s 491-day wrongful imprisonment based on sham accusations and a fake trial as part of an all-out assault on the free press and truth.”

“Evan and his family have displayed unrivaled courage, resilience and poise during this ordeal,” they added, “which came to an end because of broad advocacy for his release around the world.”

Mr. Gershkovich’s family thanked Mr. Biden and other officials who made the trade happen, along with the journalists who came to his support. “It’s hard to describe what today feels like,” the family said in a statement. “We can’t wait to give him the biggest hug and see his sweet and brave smile up close.”

Russia made it clear that the prisoner it most wanted from the West was Mr. Krasikov, the assassin imprisoned in Germany. Mr. Putin praised Mr. Krasikov when the former Fox News host Tucker Carlson asked him about Mr. Gershkovich in February. Dismissing the fact that Mr. Krasikov had been convicted of murder, Mr. Putin described him as having been motivated by “patriotic sentiments.”

In recent weeks, the court proceedings against the released Americans suddenly accelerated, suggesting that negotiations for their exchange were speeding up, too; Russia often insists that only after a verdict can an inmate be considered for trade. Russian espionage cases typically last for months, but on July 19, only the third day of trial proceedings against Mr. Gershkovich, he was convicted and sentenced to 16 years in prison.

The same day, a different Russian court convicted Ms. Kurmasheva, the Radio Free Europe/Radio Liberty editor, and sentenced her to six and a half years in prison. She had been charged with failure to register as a foreign agent, a designation Russia applied to journalists, or anyone else, receiving foreign support or subject to foreign influence.

Mr. Whelan, a former Marine and former police officer, was arrested in a Moscow hotel; prosecutors said he had a flash drive containing classified information supplied by a Russian contact. His Russian lawyer said Mr. Whelan thought the drive contained travel photos and videos.

At the time, Mr. Whelan worked in corporate security for an American auto-parts maker, BorgWarner, and had traveled several times to Russia. Relatives said that he had developed friendships with Russians, and that when he was arrested, he was there to attend a wedding.

The prisoner exchange left open the fates of other Americans and dissidents remaining in Russian prisons. In June, a court sentenced Yuri Malev, who holds American and Russian citizenship, to three and a half years in prison after he criticized the war in Ukraine on social media.

In July, Michael Travis Leake, an American rock musician, was sentenced to 13 years after prosecutors accused him of organizing a drug-trafficking ring. And Marc Fogel, a teacher at the Anglo-American School of Moscow, was sentenced in 2022 to 14 years in a penal colony on cannabis charges.

In a statement, Mr. Fogel’s relatives expressed dismay that he had not been part of the swap.

“It is inconceivable to us that Russian dissidents would be prioritized over U.S. citizens in a prisoner exchange,” they said. “Marc has been unjustly detained for far too long and must be prioritized in any swap negotiations with Russia, regardless of his level of notoriety or celebrity.”

Reporting was contributed by Richard Pérez-Peña, Ivan Nechepurenko, Valerie Hopkins, Edward Wong, Safak Timur, Andrew Higgins, Neil MacFarquhar, Alina Lobzina, Katie Rogers and Peter Baker.

The United States on Thursday night recognized Venezuela’s opposition presidential candidate, Edmundo González, as the winner of the country’s disputed election.

The announcement, by Secretary of State Antony J. Blinken, comes despite a claim by the country’s authoritarian president, Nicolás Maduro, and by the government-controlled electoral body, that Mr. Maduro had won the Sunday election.

Mr. Maduro has yet to produce clear evidence of a victory, and election officials have failed to provide a vote count. Mr. González’s campaign says it has receipts from more than 80 percent of voting machines that indicate he won by an insurmountable margin.

While some leaders have voiced support for Mr. González in recent days, the United States is the largest nation to recognize him as the winner.

The decision is sure to anger Mr. Maduro, who has long characterized Washington as meddling imperialists. But it’s unclear if the announcement will have any effect on Mr. Maduro’s grip on power.

Mr. Blinken, in a statement, said that “given the overwhelming evidence, it is clear to the United States and, most importantly, to the Venezuelan people that Edmundo González Urrutia won the most votes.”

“We congratulate Edmundo González Urrutia on his successful campaign,” Mr. Blinken continued. “Now is the time for the Venezuelan parties to begin discussions on a respectful, peaceful transition in accordance with Venezuelan electoral law.”

Mr. Maduro did not immediately respond to the statement. But just as it was issued, he wrote on X, the social media platform, that he was willing to talk to the United States “if the U.S. government is willing to respect sovereignty and stop threatening Venezuela.”

The candidacy of Mr. González, who is backed by a popular opposition leader, María Corina Machado, posed the most significant electoral threat to Mr. Maduro since he took office in 2013.

The movement that Mr. Maduro leads, known as Chavismo, has controlled Venezuela for a quarter-century, since his predecessor, President Hugo Chávez, was elected, eventually promising a socialist revolution. Under their leadership, the government has become authoritarian, arresting dissidents, crushing protests through force and crafting elections in favor of the ruling party.

Since the election, angry supporters of Mr. González and Ms. Machado have taken to the streets to protest, leading to a crackdown by security forces and armed pro-government gangs. At least 17 people have died, according to a human rights group, Foro Penal, and reporting by The New York Times. About 750 people have been arrested, according to the country’s attorney general.

Ms. Machado has called supporters to march on Saturday in Caracas, the capital, and to hang the flag of Venezuela as a “symbol of freedom.”

While the United States is not alone in doubting the election results, other nations have taken a softer approach to Mr. Maduro, clearly believing that they can use diplomacy to cajole him into releasing vote tallies from all the polling stations, as has been done in past elections, and recognizing the real result.

On Thursday, the governments of Mexico, Brazil and Colombia — all governed by leftists who have maintained relatively friendly ties with Mr. Maduro — issued a “call to the electoral authorities of Venezuela to move forward expeditiously and publicly release the data broken down by voting station.”

“We reiterate our willingness to support the efforts of dialogue and search for agreements that benefit the Venezuelan people,” the three governments said in a joint statement.

Early Monday, hours after polls closed, the government-controlled election authority said that Mr. Maduro had received 51 percent of the vote, and Mr. González 44 percent.

The opposition campaign, however, said it had collected receipts printed by each polling machine at the end of the day, and that it had gathered receipts from 81 percent of the machines. Their count indicates that Mr. González won 67 percent of the vote.

Steve Levitsky, an expert on democracy at Harvard University, has called Mr. Maduro’s assertion of victory “one of the most egregious electoral frauds in modern Latin American history.”

Mr. Blinken’s declaration that Mr. González won is likely to be welcomed by those who wanted Washington to take a strong stance. But in light of recent history, there is sure to be skepticism that the statement will have much effect.

In 2019, the Trump administration backed a claim by Juan Guaidó, then the head of Venezuela’s legislature, that he was the rightful president. Mr. Guaidó had invoked an article of the Constitution that allows the president of the National Assembly to take over the executive position in certain situations.

The move was supported by dozens of other countries, and for a brief moment it looked like Mr. Maduro might be forced out. But popular and political momentum behind Mr. Guaidó fizzled, and Mr. Guaidó fled to the United States last year. Today, Mr. Maduro points to the episode as evidence of his strength, and of American weakness.

This week, Mr. Maduro turned to the Supreme Court, which is controlled by his allies, to mediate the election dispute. The court has called for Mr. Maduro and Mr. González to appear before it on Friday.

The convicted assassin who was the linchpin of the biggest prisoner swap in decades is a member of the most powerful security agency in Russia, the Kremlin acknowledged on Friday, and had served in a special unit with some agents who now guard President Vladimir V. Putin.

The ties help explain Mr. Putin’s determination to free the assassin, Vadim Krasikov, from the German prison where he was serving time for murder. The effort culminated on Thursday when Mr. Krasikov and seven other former prisoners returned to Moscow after an exchange with Western nations that involved 24 adults and seven countries.

This was the first time that Moscow had admitted that Mr. Krasikov had been working for the Russian state in the Federal Security Service, or F.S.B., an agency that is a successor to the Soviet K.G.B., in which Mr. Putin served in the early stage of his career. The F.S.B. was also the agency that was at the center of the negotiations with the C.I.A. about the swap, Dmitri S. Peskov, the Kremlin spokesman, said.

Mr. Putin has not hid his admiration for Mr. Krasikov, who had been jailed in Germany since 2019 for the murder of a Chechen former separatist fighter in Berlin. In an interview in February, Mr. Putin referred to Mr. Krasikov as “a patriot” who was doing his duty by eliminating an enemy of the Russian state.

When the freed prisoners arrived at Vnukovo International Airport in Moscow at about 10:30 Thursday night, Mr. Putin hugged Mr. Krasikov, the first of the freed to disembark the plane.

Mr. Peskov said that it was “very important” for Mr. Putin to greet the freed Russian prisoners in person.

“This is a tribute to those people who serve their country,” Mr. Peskov told reporters during a briefing by telephone. “After difficult ordeals they got the opportunity — thanks to the very hard work of many, many people — to return to their homeland.”

Mr. Peskov also revealed that the two children of Artyom and Anna Dultsev, who had served as undercover spies in the Russian “illegals program” and were imprisoned in Slovenia, had learned only while on the plane to Moscow that they were Russian and “had anything to do” with Russia.

The children apparently believed they were Argentine, since their parents had posed in Slovenia as a couple from Argentina.

Mr. Krasikov and the other returnees received a hero’s welcome from Mr. Putin, who made a rare trip to the airport to greet them.

The Russian-made government plane pulled up in front of the V.I.P. terminal reserved for foreign dignitaries. Holding their rifles, officers of the honor guard flanked the red-painted pathway that leads toward the terminal building.

Mr. Putin stood next to the plane’s ramp, its steps covered with a red carpet, as his aides held flowers for him to give to Ms. Dultseva and her daughter.

In the past years, Mr. Putin hasn’t traveled to the airport even to greet foreign leaders, including President Xi Jinping of China last year, and his presence underscored how he viewed the swap as a personal triumph and a show of support for loyalists who carried out his wishes.

Inside the terminal, Mr. Putin thanked those prisoners “who are directly related to military service” for their loyalty to their “oath, duty and the Motherland.” He promised to decorate them with state awards and discuss their future in Russia.

A turning point came on June 25, when a group of C.I.A. officers sat across from their Russian counterparts during a secret meeting in a Middle Eastern capital.

The Americans floated a proposal: an exchange of two dozen prisoners sitting in jails in Russia, the United States and scattered across Europe, a far bigger and more complex deal than either side had previously contemplated but one that would give both Moscow and Western nations more reasons to say yes.

Quiet negotiations between the United States and Russia over a possible prisoner swap had dragged on for more than a year. They were punctuated by only occasional glimpses of hope for the families of the American prisoners — including Evan Gershkovich, a reporter for The Wall Street Journal, and Paul Whelan, an American security contractor — growing increasingly impatient for their ordeal to end. Those hopes were always dashed when one of the two sides balked.

But the June meeting changed things, according to accounts from American and Western officials and other people familiar with the long process of bringing the deal to fruition.

The Russian spies took the proposal back to Moscow, and only days later the C.I.A. director was on the phone with a Russian spy chief agreeing to the broad parameters of a massive prisoner swap. On Thursday, seven different planes touched down in Ankara, Turkey, and exchanged passengers, bringing to a successful close an intensive diplomatic effort that took place almost entirely out of public view.

The deal between longtime adversaries — negotiated mostly by spies and sometimes through secret messages hand-delivered by couriers — secured the release of Mr. Gershkovich, Mr. Whelan and 14 other imprisoned Americans, Russians and Europeans.

The deal also freed, among others, a Russian hit man, Vadim Krasikov. He had been jailed in Germany since 2019 for the murder of a Chechen former separatist fighter in a park in Berlin. He was the prize most sought by President Vladimir V. Putin of Russia, who had publicly praised the killing as an act of patriotism and for years had insisted that Mr. Krasikov be part of any swap.

The stunning deal took place against the geopolitical backdrop of the bloody war in Ukraine, where the United States is sending deadly weapons to the battlefront aimed at killing as many Russian troops as possible.

And it reached its conclusion even as President Biden, who got personally involved in the negotiations at key points, was slowly losing hope of continuing his re-election bid following a disastrous televised debate that took place two days after the C.I.A. gave the Russians what proved to be the decisive new offer.

On the morning of Sunday, July 21, Mr. Biden, sick with Covid, placed a call from his vacation home in Delaware to Slovenia’s prime minister to nail down one of the last pieces of the prisoner agreement. Less than two hours later, he announced he was withdrawing from the presidential race.

“The deal that made this possible was a feat of diplomacy and friendship,” Mr. Biden said on Thursday in brief remarks from the White House, flanked by family members of the prisoners. He praised America’s allies, saying that “they stood with us, and they made bold and brave decisions, released prisoners being held in their countries.”

“This is a very good afternoon,” said Mr. Biden, who has had few of those in the past several months. “A very good afternoon.”

American officials on Thursday insisted that the prisoner swap was by no means the advent of a new détente between Washington and Moscow. Instead, they maintained, it was a deal driven by cold calculations of national interest, a deal in which every side got something it wanted.

If it demonstrated the potential of diplomacy, it also carried a more chilling message from Mr. Putin, the former spymaster: He could succeed in snatching and holding Americans and other Westerners hostage in the service of recovering those he sends abroad to do the dirty work of the Russian state.

Something to Bargain With

In December 2022, authorities in the small, Central European country of Slovenia made two arrests that might, at first, have seemed of little consequence. They brought in a couple posing as Argentine émigrés in the country, living under the pseudonyms Ludwig Gisch and Maria Mayer, who were living a quiet life in the Slovenian capital.

As it turns out, the couple were Russian “illegals,” deep-cover intelligence officers sent abroad to spy on foreign governments.

The arrests would prove critical for the prisoner exchange. At the time, the United States had been trying to secure the release of Mr. Whelan — who had been arrested in Russia four years earlier on espionage charges — but were always unsuccessful because there was nobody in American custody the Russians believed was worthy of a swap.

Now, with the arrests in Slovenia, American officials figured they had something to barter.

The following month, in January 2023, C.I.A. officials held secret talks with Russian spies to offer a deal: Mr. Whelan’s release in exchange for the couple arrested in Slovenia. The Russians rejected the offer, but made it clear that they were willing to negotiate if the Americans offered more.

This channel had opened years earlier, when Mr. Biden and Mr. Putin agreed during a summit in June 2021 in Geneva to have their intelligence services communicate occasionally on prisoner issues.

James P. Rubin, a State Department special envoy, and Roger D. Carstens, the department’s chief hostage negotiator and a holdover from the Trump administration, came up with a plan that they called “enlarging the problem” — rather than seek a one-for-one or two-for-one exchange, they would broaden any potential swap to include many more people on both sides.

They took the idea to Secretary of State Antony J. Blinken, who carries an index card in his suit pocket every day with the names of more than 70 Americans wrongfully detained overseas — those who have been freed are in red, while those still held are in black. Mr. Blinken then took the proposal to the Oval Office in March 2023 and got Mr. Biden to approve it during a one-on-one meeting.

But the ground in the negotiations shifted later that month when the Russians arrested Mr. Gershkovich — a seasoned reporter for The Wall Street Journal covering Russia — and falsely accused him of spying for the United States.

The arrest brought one of America’s most influential news organizations into the middle of a diplomatic chess game. The day after Mr. Gershkovich’s arrest, on March 30, 2023, Jake Sullivan, Mr. Biden’s national security adviser, briefed the president about the case. Mr. Biden directed him to lead an effort to make a deal with the Russians to get Mr. Gershkovich and Mr. Whelan released.

For several days, White House officials were careful not to use C.I.A. or other intelligence contacts to inquire about Mr. Gershkovich, fearful that it would appear to the Russians that the United States was acknowledging that he was a spy. But it quickly became obvious that the Russians were already treating him like one.

During a phone call, Sergei V. Lavrov, the Russian foreign minister, bragged to Mr. Blinken that Mr. Gershkovich had been caught “red-handed” and that being a journalist did not ensure him immunity, according to a person familiar with what took place during the call.

Mr. Blinken called the spying charges outrageous and false, telling Mr. Lavrov that “we are both adults” who know that the United States does not use journalists to commit espionage.

But it was becoming clearer to the Americans what the Russians really wanted: the release of Mr. Krasikov. To Mr. Putin, the convicted assassin, who had kept his mouth closed throughout his murder trial in Germany, had become “a symbol” of a faithful soldier carrying out his duty to the Russian state, said a person close to the Kremlin who was involved in some of the talks on a prisoner exchange.

Mr. Putin, the person said, saw Mr. Krasikov as a man who had been “carrying out a mission of state importance.” Winning his freedom would be “a signal to all the guys that we won’t leave you behind,” the person said.

Mr. Rubin heard from Christo Grozev, who had been the lead Russia investigator for Bellingcat, a research group that had exposed Russian wrongdoing, that Mr. Krasikov was the key to a deal. He was not just a Russian agent but was also personally close to Mr. Putin, someone the Russian president considered a friend, Mr. Rubin was told.

Mr. Putin had even spoken publicly about his interest in getting Mr. Krasikov released, during an interview in February with Tucker Carlson, the conservative commentator.

“Over the course of this negotiation, we did reach the conclusion that Krasikov was a key,” Mr. Sullivan told reporters on Thursday.

But including Mr. Krasikov in any prisoner deal meant persuading the German government to give him up, a move that posed significant political risk for Chancellor Olaf Scholz. The Americans had already tried once to get the Germans to trade Mr. Krasikov for Mr. Whelan and been rebuffed.

In April 2023, weeks after Mr. Gershkovich’s arrest, Mr. Blinken gauged the German foreign minister’s interest in a possible deal that, besides the imprisoned Americans and the Russian assassin, would also include the release of Aleksei A. Navalny, the prominent Russian dissident whom the Germans had been working to get freed from a Russian prison.

The German foreign minister, Annalena Baerbock, was cool to any plan that led to the freedom of Mr. Krasikov out of concern that it would encourage more hostage-taking, so White House officials decided to engage the chancellor’s office directly.

In the months that followed, Mr. Sullivan spoke regularly with his counterpart in Berlin. The two men passed lists of possible prisoners to be exchanged — documents given highly classified, “eyes-only” designations — back and forth between Washington and Berlin.

‘For You, I Will Try to Do This’

Without Mr. Krasikov as part of a deal, there was no deal to be had. American officials spent months looking for other Russians in captivity to trade. Last November, C.I.A. officers based in Moscow offered another deal — Mr. Whelan and Mr. Gershkovich for four Russian spies under arrest, including the two arrested in Slovenia — but the Russians rejected it.

Throughout last year and into this year, the White House kept up discussions with the German government, even as it looked for more prisoners to trade. One official examined the possibility of a Russian being held in Brazil. Another looked into someone in Kuwait.

Mr. Carstens, the hostage negotiator, was in Tel Aviv last November and heard that Roman Abramovich, a Russian oligarch close to Mr. Putin, was in town. The two agreed to meet in a seaside hotel and Mr. Carstens asked whether Mr. Putin would be open to a trade of Mr. Krasikov for Mr. Navalny.

Mr. Abramovich said he did not think so. But then he called back a week later and said that he had checked and that, to his own surprise, Mr. Putin would be open to such a deal.

On Jan. 16, Mr. Biden spoke by phone to Mr. Scholz, who finally relented, agreeing to include Mr. Krasikov in a prisoner deal as long as it also included Mr. Navalny.

“For you, I will try to do this,” Mr. Scholz told the president. At a meeting in the Oval Office on Feb. 9, the two men agreed to pursue the idea, according to an American official.

The optimism would not last long. Mr. Navalny died in a Russian penal colony a week later, before the United States had formally broached the possibility of including him in a prisoner deal with the Russians. With the shock and sadness of Mr. Navalny’s death also came the realization that the deal was now farther away.

That same day, Mr. Sullivan kept a previously scheduled meeting with Mr. Gershkovich’s parents in his office in the West Wing. While Mr. Navalny’s death seemed to extinguish hope for a quick deal, senior American officials remained optimistic in part because Germany had already agreed in principle to give up Mr. Krasikov. It was only a matter of time, these officials felt, before they found another way to structure a deal around him.

“I saw his parents, and I told them that the president was determined to get this done, even in light of that tragic news, and that we were going to work day and night to get to this day,” Mr. Sullivan said on Thursday in recounting his conversation with Mr. Gershkovich’s mother and father.

The White House once again had to work to persuade the German chancellor to include Mr. Krasikov in a revised prisoner deal.

It took weeks to develop the outlines of a proposal shared with the German government, one including numerous people in Russian prisons whom the Germans wanted released, including former associates of Mr. Navalny. The Americans added Vladimir Kara-Murza, another imprisoned Russian dissident, who was also a permanent U.S. resident, as a sort of substitute for Mr. Navalny to appeal to Mr. Scholz’s desire for a moral imperative to justify the release of a Russian assassin.

The proposal also needed commitments from Slovenia, Norway and Poland that Russian spies imprisoned in those countries would be released as part of the deal.

Hard copies of the proposal were traded back and forth by courier, though on at least one occasion the “eyes-only” document for Jens Plötner, Germany’s national security adviser, was deemed undeliverable because Mr. Plötner was on vacation. (The document was returned to sender in the United States.)

In April, Mr. Biden sent the German chancellor the outlines of the proposal in a letter.

Then, at the White House Correspondents’ Association dinner later that month, Mr. Gershkovich’s mother, Ella Milman, made a direct appeal to the president when she got a chance to speak briefly with him there, urging him to push Mr. Scholz for more help in working out a deal for her son.

Mr. Scholz approved the deal to include Mr. Krasikov on June 7, and on June 25 the C.I.A. officers made the proposal to the Russians in the Middle East. The deal that the Russians agreed to was largely the same as the June 25 proposal, American officials said.

Early last month, William Burns, the C.I.A. director, spoke with Aleksandr V. Bortnikov, the head of Russia’s F.S.B. intelligence service. Days later, C.I.A. officials and Russians intelligence operatives met again in person, this time in Turkey, to work out the final details of the agreement.

Stage-Managed Trials, Disappearing Prisoners

In Russia, a hint that a deal might be close came on July 19, when Mr. Gershkovich was sentenced to 16 years in prison after the court suddenly accelerated his trial. The surefire guilty verdict, which had been expected to take months to arrive, was handed down after just three hearings.

The same day, Alsu Kurmasheva, a Russian American journalist who was also released on Thursday as part of the deal, was similarly convicted in a surprisingly speedy trial.

In Russia, the accelerated, stage-managed trials were seen as important signs of a possible prisoner exchange, as Russian officials had said they would trade only convicted prisoners.

Then, last Sunday, the husband of Lilia Chanysheva, a Russian political activist behind bars in the Ural Mountains, arrived at her prison on a routine visit to bring her a package. He received worrying news: As of two days earlier, he was told, Ms. Chanysheva was no longer there.

The husband, Almaz Gatin, pleaded for help online and, with lawyers, scoured three jails and one other prison. “She’s nowhere to be found!” he wrote.

By this past Tuesday, a total of six Russian political prisoners had been reported missing. Relatives of the Russians who would be freed in the swap said they were kept in the dark about their loved ones’ fates — even as the exchange played out online in live footage from the Ankara airport showing a large Russian government plane parked next to smaller private jets.

Tatiana Usmanova, the wife of the imprisoned opposition politician Andrei Pivovarov, said she felt anxious as the drama unfolded, hoping — but not knowing — that her husband had been on that Russian plane. It was only after 7 p.m. Moscow time, nearly two hours after the Russian plane landed in Turkey, that her husband called her from Ankara.

“It felt so new,” Ms. Usmanova said. “We hadn’t spoken on the phone for three years and two months.”

Stepping off another plane in Ankara on Thursday were “Ludwig Gisch” and “Maria Mayer,” the two Russian spies posing as an Argentine couple who were arrested in Slovenia in 2022.

Their real names are Artem Dultsev and Anna Dultseva. After a short time on the tarmac, they boarded the Russian government plane along with the other six Russians released by the West.

Hours later, in a remarkable moment for the reclusive Russian president, Mr. Putin embraced a tearful Ms. Dultseva as she stepped off the plane in Moscow and handed her an oversize bouquet of white, pink and purple flowers.

In a near-mirror image, Mr. Biden and Vice President Kamala Harris stood on the tarmac at Joint Base Andrews outside Washington late Thursday as the freed Americans arrived home.

Ekaterina Bodyagina contributed reporting from Berlin, Valerie Hopkins from Paris and Alina Lobzina from London.

Standing in front of a lectern on Thursday, his voice at times taut with anger, Britain’s prime minister announced a crackdown on what he called the “gangs of thugs” who instigated violent unrest in several towns this week.

But the question of how to confront one of the key accelerants — a flood of online misinformation about a deadly stabbing attack — remained largely unanswered.

Prime Minister Keir Starmer called out online companies directly, after false information about the identity of the 17-year-old suspected in the attack spread rapidly on their platforms, no matter how many times police and government officials pushed back against the claims.

Three girls died after the attacker rampaged through a dance class in Southport, northwest England, on Monday. Of the eight children injured, five remain in the hospital, along with their teacher, who had tried to protect them.

Immediately after the attack, false claims began circulating about the perpetrator, including that he was an asylum seeker from Syria. In fact, he was born in Cardiff, Wales, and had lived in Britain all his life. According to the BBC and The Times of London, his parents are from Rwanda.

The misinformation was amplified by far-right agitators with large online followings, many of whom used messaging apps like Telegram and X to call for people to protest. Clashes followed in several U.K. towns, leading to more than 50 police officers being injured in Southport and more than 100 arrests in London.

Officials fear more violence in the days ahead. The viral falsehoods were so prevalent that a judge took the unusual step of lifting restrictions on naming underage suspects, identifying the alleged attacker as Axel Rudakubana.

“Let me also say to large social media companies and those who run them: Violent disorder, clearly whipped up online, that is also a crime, it’s happening on your premises, and the law must be upheld everywhere,” Mr. Starmer said in his televised speech, though he did not name any company or executive specifically.

“We will take all necessary action to keep our streets safe,” he added.

The attack in Southport, England, has been a case study in how online misinformation can lead to actual violence. But governments, including Britain, have long struggled to find an effective way to respond. Policing the internet is legally murky terrain for most democracies, where individual rights and free speech protections are balanced against a desire to block harmful material.

Last year, Britain adopted a law called the Online Safety Act that requires social media companies to introduce new protections for child safety, while also forcing the firms to prevent and rapidly remove illegal content like terrorism propaganda and revenge pornography.

But the law is less clear about how companies must treat misinformation and incendiary, xenophobic language. Instead, the law gives the British agency Ofcom, which oversees television and other traditional media formats, more authority to regulate online platforms. Thus far, the agency has not taken much action to tackle the issue.

Jacob Davey, a director of policy and research at the Institute for Strategic Dialogue, a group that has tracked online far-right extremism, said many social media platforms have internal policies that prohibit hate speech and other illicit content, but enforcement is spotty. Other companies like X, now owned by Elon Musk, and Telegram have less moderation.

“Given the confrontational tone set by some companies it will be challenging to hold them accountable for harmful but legal content if they decide they don’t want to enforce against it,” said Mr. Davey.

The European Union has a law called the Digital Services Act that requires the largest social media companies to have robust content moderation teams and policies in place. With the new powers, regulators in Brussels are investigating X and have threatened to fine the company in part for its content moderation policies.

In the United States, where free speech protections are more robust than in Europe, the government has few options to force companies to take down content.

X could not be reached for comment, though Mr. Musk replied “insane” to a video on X of Mr. Starmer’s remarks. Meta, owner of Facebook and Instagram, did not respond to a message seeking comment.

Telegram said that calls to violence are “explicitly forbidden” on its platform and that it was developing a tool that would allow fact-checkers within a country to add verified information to posts that are being viewed by users in that territory.

British policymakers said the country must address false information spread by the far right on social media.

“I see it almost every single day — straight-up lies about these situations designed to cause violence, to incite racial hatred, to incite people to violence,” Jonathan Brash, a member of Parliament from Hartlepool, an area where there were violent clashes with the police, said Thursday on BBC Radio 4. “There is so much misinformation and it’s being spread quite deliberately to stoke tension in communities.”

Al Baker, the managing director of Prose Intelligence, a British company that provides services for monitoring Telegram, said the online discourse was a reflection of wider societal challenges.

“It’s important not to go too far and say the internet is the cause,” Mr. Baker said. “The internet and social media are an accelerant that intensify existing problems we have as a society.”

Olympic officials on Friday tried urgently to rebut what they described as widespread “misinformation” that had turned a 46-second Olympic boxing match at the Paris Games into a forum for fierce debates and complicated questions about biology and competitive advantage in women’s sports.

Mark Adams, the chief spokesman for the I.O.C., derided news articles and social media posts that he said sought to cast doubt — unfairly, in the view of Olympic officials and even some other competitors — on the gender of one of the boxers in the women’s competition, Imane Khelif of Algeria. Mr. Adams stressed at a news conference that Khelif is not transgender.

“There has been some confusion that somehow it’s a man fighting a woman,” Mr. Adams said.

“The question you have to ask yourself is, are these athletes women?” he added. “The answer is yes,” according to their eligibility, passport and history.

Khelif won her opening bout on Thursday when her Italian opponent, Angela Carini, refused to continue, and after she was cleared to compete in the Olympics despite being suddenly disqualified during last year’s world championships in a dispute about her eligibility.

Thursday’s fight ended after less than a minute when Carini abandoned the bout after taking a powerful punch to the face. Khelif, who had boxed as a woman for her entire career with occasional success, will fight next in the quarterfinals on Saturday.

Carini later told reporters that the controversy over her defeat “makes me sad” and that she was worried about the focus on Khelif. “If the I.O.C. said she can fight, I respect that decision,” she said.

But the fallout from Khelif’s victory, and Carini’s comments immediately afterward about the force of her punches, brought new scrutiny to the various and sometimes minimal and vague rules regarding eligibility for some women’s sports, as well as to a fractious dispute between the International Olympic Committee and the former governing body for boxing at the Olympic Games.

Even as he defended Khelif, Mr. Adams acknowledged a lack of scientific, political and social consensus about how to resolve eligibility issues across women’s sports.

“It’s not a black-and-white issue,” he said, referring to the topic as “a minefield.”

At the same time, he cautioned, “If we start acting on every issue, every allegation, that comes up, then we start having the kind of witch hunts that we’re having now.”

Sex testing began at the Olympics in 1968 and was halted in 2000. The I.O.C. has left it up to individual sports governing bodies to determine their own eligibility rules.

Boxing at the Paris Olympics is being overseen by a temporary body set up by the I.O.C. after the International Boxing Association was stripped of its authority as a governing body in June 2023. But the tournament itself is being held under rules established by the I.B.A., and those regulations essentially determine competitors’ eligibility by the sex listed on an athlete’s passport.

Still, Khelif and another boxer, Lin Yu-ting of Chinese Taipei, were disqualified during the 2023 world boxing championships by a murky process that the I.O.C. has called arbitrary and unfair. The decision has never been fully explained by boxing officials. Lin, a former world champion, won her opening bout on Friday but declined to speak to reporters afterward.

Both athletes have competed in women’s boxing for years, including at the Tokyo Olympics, at which neither won a medal. The widespread criticism of them now, even before Lin had entered the ring, had been “pretty emotionally damaging” to them, Mr. Adams said.

The president of the boxing association, Umar Kremlev of Russia, told the Tass news agency after the 2023 world championships that Khelif and Lin had been disqualified during that competition because they possessed X and Y chromosomes, the typical male pattern.

It is not clear if Mr. Kremlev was referring to what is called a difference of sexual development known as 46XY DSD. Athletes with the condition are legally female or intersex; have the typical male pattern of chromosomes; testes or ambiguous genitalia; testosterone in the male range; and the ability to respond to testosterone in ways typical to men.

Minutes of a boxing association meeting held shortly after the 2023 disqualification appear to show that the ouster was decided solely by the association’s chief executive and later ratified by its board. The minutes also stressed the need for the boxing association to establish “a clear procedure on gender testing.”

Christian Klaue, another I.O.C. spokesman, said on Friday, “You cannot just come out and disqualify somebody and say, OK, we don’t have rules and we establish the rules afterward.”

According to the minutes of the meeting, Khelif and Lin also failed eligibility requirements at the 2022 world championships in Istanbul, but testing results were not received until the conclusion of the competition, so the athletes were not disqualified.

The two were allowed to compete at the 2023 world championships but then disqualified during the competition. The nature of the testing administered in 2023 and 2023 remains unclear.

According to the boxing association, Khelif initially appealed her disqualification last year to the Court of Arbitration for Sport “but withdrew the appeal during the process, making the I.B.A. decision legally binding.” Lin did not challenge her disqualification.

Referring to the 2023 disqualifications, Mr. Adams of the I.O.C. expressed skepticism about the legitimacy of the testing undergone by Khelif and Lin. “We don’t know what the protocol was,” he said. “We don’t know whether the test is accurate. We don’t know whether we should believe the test.”

Some Olympic officials have noted that Khelif’s disqualification in 2023 came after the Algerian defeated a Russian boxer, though there has been no proof that this caused Khelif’s ouster.

Before decertifying the International Boxing Association, the I.O.C. expressed concern about the association’s heavy reliance for funding on Gazprom, the Russian energy giant, as well as its concern about scandals involving refereeing and judging.

While suspended in 2023, the boxing association invited Russian athletes to compete under their own flag at the world championships in New Delhi, contravening I.O.C. recommendations after Russia’s invasion of Ukraine. Three months later, the Olympic committee withdrew the authority of the International Boxing Association to oversee the sport at the Paris Games.

In an interview on Thursday, Claressa Shields, the first American woman to win an Olympic gold medal in boxing, suggested that testing for testosterone levels was a potential way to offer clarity on a complex issue. But, like Olympic officials, she acknowledged that simple solutions were impossible, and warned that “we can’t punish a woman for naturally having something that other women don’t have.”

“My stance is, men should fight against men, women should fight against women, and transgenders should fight against transgenders if there are any fighting in the Olympics,” Shields said. “But this situation here, it was woman vs. woman, so that’s were the confusion is coming in for me.”

The I.O.C. said Friday it hopes that another international federation will be certified so that boxing can remain part of the Olympic program at the 2028 Olympics in Los Angeles.

Simone Biles won her second career Olympic all-around title on Thursday by more than a full point after recovering from a mistake on the uneven bars to fend off a strong challenge from Rebeca Andrade of Brazil, who won the silver medal.

Vault

Biles performed the world’s most difficult vault, the Yurchenko double pike, which no other woman has done. The difficulty value gave her a cushion of eight-tenths of a point over Andrade, who performed a vault called a Cheng. While Andrade’s vault was nearly flawless and Biles took a step backward on her landing, that cushion put Biles solidly in the lead after the first rotation.

Bars

Biles made a significant mistake on the uneven bars, positioning herself incorrectly on a transition from the high bar to the low bar such that she had to bend her legs to avoid hitting the mat and then do an extra swing to regain her rhythm. It was a big enough error that Andrade and Kaylia Nemour of Algeria both pulled ahead of her, leaving her in third place at the halfway point of the competition. Biles’s teammate Sunisa Lee, meanwhile, started to make up ground.

Beam

All of the eventual medalists had at least slight wobbles on the balance beam, but Biles kept hers to a minimum and pulled back into the lead, capping her routine with an extremely difficult full-twisting double back dismount. Andrade, whose routine was a little less difficult than Biles’s and who had slightly more severe execution errors, remained within a couple tenths of a point of her, keeping the pressure on heading into the final rotation.

Floor

With her distinct floor routine, Biles cemented her lead and became the first woman in more than half a century to win two Olympic all-around titles. The routine included two skills named after her: a triple-twisting double back flip with her knees tucked to her chest, and a half-twisting double back flip with her body straight. Andrade stepped out of bounds once but held on to place second, and Lee hit a solid routine for bronze.

Lee, the all-around champion at the Tokyo Games in 2021, hit a solid routine that guaranteed her the bronze medal, starting with a full-twisting double back flip that she landed so well that she looked visibly thrilled as her feet hit the ground. By the time the last score was announced, Biles and Lee already knew what it would show. They were waiting by the side of the floor with an American flag for the moment it became official.