Prime Minister Benjamin Netanyahu slammed his defense minister on Monday, exposing deep rifts within the Israeli government as the Middle East entered a high-wire week, suspended between the prospect of a wider regional conflict and intensive diplomatic efforts to prevent one.

Mr. Netanyahu criticized the defense minister, Yoav Gallant, after Israeli news media reported that Mr. Gallant had disparaged his goal of achieving a “total victory” over Hamas in the Gaza Strip by telling lawmakers in a private security briefing on Monday that it was “nonsense.”

“When Gallant adopts the anti-Israel narrative, he harms the chances of reaching a hostage-release deal,” the prime minister’s office said in a statement. Victory over Hamas and the release of hostages, the statement said, is the “clear directive of Prime Minister Netanyahu and the cabinet, and it obligates everyone — including Gallant.”

The public scolding came as the Middle East braced for a possible escalation in violence and the United States continued its military buildup in the region, dispatching the guided-missile submarine Georgia there.

Iran and its most powerful regional proxy, Hezbollah in Lebanon, have vowed to retaliate for the killings nearly two weeks ago of Hamas’s political leader, Ismail Haniyeh, in an explosion in Tehran and of a senior Hezbollah commander, Fuad Shukr, in an Israeli airstrike in the southern suburbs of Beirut.

Iran has blamed Israel for the death of Mr. Haniyeh, who was in Iran to attend the inauguration of its new president. Israel has not confirmed or denied if it was behind the attack, although U.S. officials have privately assessed that it was.

Iran’s supreme leader, Ayatollah Ali Khamenei, has promised to deliver a “severe punishment” for the assassination on Iranian soil. Mr. Netanyahu has vowed, in turn, to “exact a heavy price for any act of aggression against us, from whatever quarter.”

At a news conference clearly intended to reassure a jittery Israeli public, the chief spokesman for Israel’s military, Rear Adm. Daniel Hagari, said, “We are prepared at peak readiness in offense and defense, and we will act according to the directives of the government.”

On Monday, John F. Kirby, a national security spokesman at the White House, told reporters that President Biden had spoken to European leaders about the tensions in the region. Mr. Kirby said the United States agreed with Israel’s assessment that an attack by Iran and its proxies could happen “as soon as this week.”

He said that the White House still expected Gaza cease-fire talks to resume on Thursday, though he conceded that an Iranian attack could derail those plans. “We fully expect that to move forward, and they need to move forward,” Mr. Kirby said.

Mr. Biden, along with the leaders of Egypt and Qatar, said last week that they were prepared to present a “final” proposal for a cease-fire in Gaza at the meeting. On Monday, the White House released a joint statement from Mr. Biden and the leaders of Britain, France, Germany and Italy endorsing the effort to broker a cease-fire on Thursday, saying, “There is no further time to lose.”

The leaders also “called on Iran to stand down its ongoing threats of a military attack against Israel.”

Several senior Biden administration officials are fanning out across the Middle East this week to make a full-court press to nail down a Gaza cease-fire deal and, possibly, to try to avert an attack by Iran or its proxies against Israel, U.S. officials said late Monday.

The officials being dispatched include William J. Burns, the C.I.A. director, who is traveling to Qatar; Brett McGurk, Mr. Biden’s Middle East coordinator, who is heading to Egypt and Qatar; and Amos Hochstein, a senior White House adviser, who is visiting Lebanon.

Mr. Netanyahu’s office has said that Israel would send a negotiating team to the meeting, which is expected to take place in Cairo or the Qatari capital, Doha. It was unclear whether Hamas would take part in the talks. In a statement on Sunday, Hamas suggested it was not interested in participating, saying it had already agreed to a framework for a cease-fire.

In the absence of a truce, the Israeli military pressed ahead with its offensive, ordering civilians on Sunday to evacuate part of a designated safe zone it had established in southwestern Gaza, as it prepared to attack what it said was “embedded terrorist infrastructure” there. Israel’s military said it was urging civilians to move to other areas it said were safe.

But nowhere in Gaza is safe, many Palestinians say, and even the areas designated by the Israeli military as humanitarian zones lack basic necessities.

“The truth is that this area is anything but humanitarian,” said Kamel Mohammed, 36, who was sheltering in a tent with nine relatives in a coastal strip of Gaza known as Al-Mawasi.

“We do not have the means for a decent life,” Mr. Mohammed said. “No drinkable water, no healthy food, and we have resorted to building primitive bathrooms.”

Facing international condemnation for an airstrike on Saturday that hit a school compound used to shelter Palestinians in northern Gaza, Israel on Monday said that the strike had killed 31 militants. According to Gaza’s health officials, more than 100 Palestinians were killed; the Gazan tallies do not distinguish between combatants and civilians.

With the Middle East on edge, the American defense secretary, Lloyd J. Austin III, spoke to Mr. Gallant on Sunday and “reiterated the United States’ commitment to take every possible step to defend Israel,” according to the Pentagon press secretary, Maj. Gen. Patrick S. Ryder.

General Ryder also made the unusual disclosure that the submarine Georgia had been sent to the Middle East. The Pentagon rarely announces the movements of its submarine fleet, and the disclosure underscored the seriousness of the crisis. The Georgia can fire cruise missiles and carry teams of Navy SEAL commandos.

General Ryder noted that Mr. Austin had already ordered additional combat aircraft and warships capable of shooting down missiles and drones to the region. Mr. Austin has also directed the aircraft carrier Abraham Lincoln, equipped with F-35 fighter jets, to accelerate its arrival in the region, joining the aircraft carrier Theodore Roosevelt and its accompanying warships already in the Gulf of Oman.

The Lincoln is expected to arrive in the next several days, and could overlap with the Roosevelt for at least a couple of weeks, doubling the carrier firepower in the region.

“Are we trying to send a message? Absolutely,” General Ryder told reporters on Monday. “We’re looking to de-escalate tensions.”

Mr. Netanyahu’s dress-down of Mr. Gallant reflected longstanding divisions in his right-wing government over the prosecution of the war in Gaza and the fate of the approximately 115 hostages still in Gaza, an unknown number of whom have died.

Mr. Gallant, a member of Mr. Netanyahu’s Likud party, has clashed with the prime minister before.

Last year, he called on Mr. Netanyahu’s government to suspend a proposal to overhaul the Israeli judiciary after it led to widespread protests. And in May, Mr. Gallant said the lack of a postwar plan for governing Gaza could force Israel into a permanent occupation, costing it “in blood and many victims, for no purpose.”

In a statement on Monday, Mr. Gallant did not confirm or deny whether he had dismissed as “nonsense” the prime minister’s goal of “total victory” over Hamas. An Israeli lawmaker who attended Mr. Gallant’s security briefing confirmed, however, that the defense minister had used the term.

“During a security briefing I gave today to the Foreign Affairs and Defense Committee,” Mr. Gallant said in the statement, “I emphasized I was determined to achieve the war’s goals and continue fighting until Hamas is dismantled and the hostages are returned.”

Despite Mr. Netanyahu’s rebuke of Mr. Gallant, he was not planning to fire him as defense minister, according to an Israeli official who spoke on the condition of anonymity and was not authorized to communicate with reporters.

Reporting was contributed by Hiba Yazbek, Ameera Harouda, Abu Bakr Bashir, Patrick Kingsley, Julian Barnes, Adam Entous and Michael D. Shear.

The scenes were decidedly Russian. A Gazprom facility. Flags with the country’s signature three horizontal stripes of white, blue and red. A Pyatyorochka supermarket.

The soldiers posting the videos, verified by The New York Times, were Ukrainian, almost giddily showing off just how easily they had pushed over the border and through Russian lines of defense in the past week.

In the Russian town of Sverdlikovo, a Ukrainian soldier climbed onto another’s shoulders, broke off the wooden post anchored to a town council building and threw the Russian flag to the ground. In Daryino, a town five miles to the west, other soldiers also grabbed a Russian flag. “Just throw it away,” a Ukrainian soldier said, grinning, as another flexed his muscles.

On Aug. 6, Ukraine launched an audacious military offensive, planned and executed in secrecy, with the aim of upending the dynamics of a war it has appeared to be losing, town by town, as Russian troops have ground forward in the east. The operation surprised even Kyiv’s closest allies, including the United States, and has pushed the limits of how Western military equipment would be permitted to be used inside Russian territory.

For Russia, it was a moment nearly as shocking as the mercenary Yevgeny V. Prigozhin’s march on Moscow in June 2023: the vaunted security state that President Vladimir V. Putin had built crumbled in the face of the surprise attack, failing in its basic task of protecting its citizens. And the unwritten social contract that has largely accompanied Mr. Putin’s 30-month campaign — that most Russians could get on with their normal lives even as he waged war — was cast into question anew.

Mostly on the defensive since a failed counteroffensive last year, Ukraine has pushed seven miles into Russia along a 25-mile front and taken dozens of Russian soldiers as prisoners, analysts and Russian officials say. The governor of Russia’s Kursk region said on Monday that Ukraine controls 28 towns and villages there. More than 132,000 people have been evacuated from nearby areas, Russian officials said.

“Russia brought war to others, and now it is coming home,” President Volodymyr Zelensky of Ukraine said in his Monday night address.

This offensive is a major gamble, especially since Russia dominates much of the frontline in Ukraine and has made significant inroads in the east. If Ukrainian troops are able to hold territory, they could stretch the capacity of Russian troops, deliver a major embarrassment for Mr. Putin and get a bargaining chip for any peace negotiations. But if Russia manages to push Ukrainian troops out of Kursk and simultaneously move forward in eastern Ukraine, Ukrainian military leaders could be blamed for giving the Russians an opening to gain more ground, particularly in the Donetsk region.

U.S. officials told The Times they were given no formal heads-up about the high-risk mission — possibly because Ukrainian officials feared the Americans would try to persuade Ukraine to call it off, possibly because of Ukraine’s obsessive concern over leaks. Ukraine was also using American-supplied vehicles, arms and munitions, despite President Biden’s caution in May that Ukraine could only use American-made weapons inside Russia for limited self-defense strikes.

U.S. officials have said that Ukraine’s cross-border offensive didn’t violate that policy. “They are taking actions to protect themselves from attacks,” Sabrina Singh, the Pentagon’s deputy press secretary, said on Thursday.

Ukrainian officials have remained tight-lipped about the mission, including whether they intend to hold ground or fall back to defenses on their side of the border. Mr. Zelensky only acknowledged the operation publicly for the first time on Saturday. Ukrainian soldiers said they didn’t know the plan in advance. Military analysts who spend their days tracking the war said they were surprised.

“This is a good example of how a modern successful operation requires extreme operational security measures and deception,” said Pasi Paroinen, an analyst from the Black Bird Group, a Finland-based organization that analyzes battlefield footage. He added that if analysts couldn’t detect it, the Russians might not be able to either.

A quiet buildup

There were hints of what was to come.

Maps of the battlefield compiled by independent analysts show that soldiers from brigades long fighting in the east had moved discreetly into Ukraine’s Sumy region, just across the border from Kursk. A drone battalion from the 22nd Mechanized Brigade, which for nearly a year had defended the beleaguered frontline town of Chasiv Yar, was spotted near the border in mid-July. Troops from the 82nd Air Assault Brigade, engaged in fierce combat near Vovchansk in Ukraine’s Kharkiv region, also shifted to the area. So did soldiers from the 80th Air Assault Brigade, which was at the forefront of fighting in the Kharkiv region this spring.

A few Russians noticed. A report was submitted to Russian military leadership about a month before the attack saying that “forces had been detected and that intelligence indicated preparations for an attack,” Andrei Gurulyov, a prominent member of Russia’s Parliament and a former high-ranking army officer, said after the incursion.

“But from the top came the order not to panic, and that those above know better,” Mr. Gurulyov lamented on national television.

Any movement could have been misconstrued as a new defensive posture. The Ukrainian Army sometimes splits brigades into smaller battalions scattered across the battlefield, and Sumy has long been rumored as a place where Russia might try opening a new front.

Few expected Ukraine to be able to launch a new offensive. Ukrainian brigades were running low on ammunition. Even as new weapons started arriving this spring and summer from the West, an almost fatalistic mood had taken hold of many Ukrainians, that they were losing ground in the east, foot by foot.

Ukraine shuffled parts of brigades into the Sumy area under the pretenses of training and picking up new equipment, said one brigade’s deputy commander, Lt. Col. Artem, who asked to be identified only by his first name and rank, in keeping with military protocol.

Heavy weaponry moved in. Soldiers piled into houses. The Ukrainians hid in plain sight. Officers were told to avoid wearing military uniforms when entering towns and cities so they didn’t draw attention, said one officer, who identified himself by his call sign, “Tykhyi,” in keeping with military protocol.

Some residents noticed the buildup. “Maybe they were reinforcing the border, or maybe building something?” said Elena Sima, the head of the Yunakivka district, about five miles from the border. “Everybody was guessing.”

In the village of Khotyn, the rumble of heavy, tracked vehicles woke up Natalya Vyalina, a 44-year-old kindergarten teacher, several nights in a row. She assumed others heard it, too. But in the village, she said, “nobody said anything.”

Even within the army, many were kept in the dark. Tykhyi — which means “quiet one” in Ukrainian — said some units were told of their mission only at the last moment.

On Aug. 3, Colonel Artem said, his brigade commander summoned senior officers to a meeting on the side of a forest road to announce the mission’s goals. To divert Russian troops to help fellow soldiers fighting in the eastern Donbas region. To push Russian artillery out of range of Sumy. To demoralize the Russians by showing their intelligence and planning failures.

‘Difficult challenges ahead’

The Ukrainian military hadn’t tried a serious push into Russia since the beginning of Moscow’s full-scale invasion in 2022. Commandos had made quick forays across the border, one in May 2023 and another this March. They were claimed by two shadowy paramilitary groups with ties to Ukraine: the Russian Volunteer Corps and the Freedom of Russia Legion.

Away from the fighting, the Kursk region posed an easier target than elsewhere along the 600-mile front in the east and south of Ukraine. It had fewer anti-armored vehicle ditches, fewer of the anti-tank pyramid obstacles known as dragon’s teeth and fewer manned fighting positions, said Brady Africk, an American analyst who maps Russia’s defenses. Russia also appeared to have sown fewer mines in the Kursk region than in occupied Ukrainian territories.

“Russia’s fortifications in Kursk are less dense than in other areas where Russian forces have built formidable defenses, such as in the south,” Mr. Africk said.

Just before noon on Aug. 6, Russian authorities claimed about 300 soldiers, more than 20 armored combat vehicles and 11 tanks from Ukraine’s 22nd Mechanized Brigade had crossed into the country. But those initial reports were greeted with a shrug. Disinformation and propaganda have become another kind of front in this war, and no one thought such an incursion made any tactical sense.

Hundreds more Ukrainian forces surged forward, breaching border checkpoints and pushing through two lines of defense. With fewer mines and fewer anti-military obstacles, Ukrainian mechanized brigades moved quickly.

Oleksandr, a Ukrainian infantry soldier who declined to give his last name, citing military security protocols, said many Russian soldiers fled as the Ukrainians pushed forward. Eight Russian soldiers surrendered at one checkpoint, he added.

Early Wednesday, senior U.S. officials woke up to a shock: They learned that more than 1,000 regular Ukrainian Army forces had crossed the border the day before, equipped with mobile air defenses and electronic-warfare equipment to jam Russian radar. Some were driving in armored vehicles sent by Germany and the United States. The soldiers appeared to be planning for an extended fight.

As late as Thursday, U.S. officials said, they were still seeking clarity from Ukrainian officials on the operation’s logic and rationale. Since then, Ukrainian leaders have briefed senior U.S. civilian officials and top military commanders on their goals.

The American officials said they were surprised at how well the operation has gone so far, but were skeptical that the Ukrainians could hold onto their gains. And in making the incursion, they said, Ukraine has created new vulnerabilities along the front where its forces are already stretched thin.

Videos show Ukrainian forces may have faced resistance at times, although there is not visual evidence of widespread losses.

Outside the Russian village of Kremyanoye, a video filmed by a Russian soldier shows Russian soldiers ransacking a captured Ukrainian armored vehicle, and taking away what appeared to be ammunition and other supplies. In another video filmed a few hundred meters away, a Russian soldier tried to rip a Ukrainian flag patch from the uniform of a dead soldier lying in the grass. Other footage, posted on Telegram by Russia’s Ministry of Defense, appeared to show Russian forces firing on a Ukrainian brigade around the Kursk region.

“We all have joy in our hearts,” the Ukrainian soldier, Oleksandr, said in a phone interview at 5 p.m. on Thursday, from somewhere inside Russia. “But we realize that there are still difficult challenges ahead.”

Some Ukrainian troops haven’t been able to stop themselves from publicizing their moves. They’ve posted videos and selfies from Russian towns like Sudzha or villages like Poroz and Dmitriukov, bragging about how they have finally taken the fight to Russia.

Outside a Pyatyorochka store in Sudzha, about six miles from the Russian border, one Ukrainian soldier said that a Ukrainian supermarket chain, ATB, was much better. “Glory to Ukraine,” he said in a video, which like others were verified by The Times. “No Pyatyorochka, ATB will be here soon.”

Four Ukrainian soldiers posed outside a nearby Gazprom facility, the Russian state-owned gas monopoly.

“From Sudzha, our news is as follows: The town is controlled by the armed forces of Ukraine,” one said, holding a rifle and standing in front of three soldiers brandishing a blue-and-yellow Ukrainian flag. “Peace in the town. All houses are intact.” He added: “I wish everyone a peaceful sky.”

One video filmed by Ukrainian forces showed Ukrainian armored vehicles gliding along roads and through open fields in the Kursk region. Another showed a convoy of a dozen or so burned Russian vehicle husks near the town of Rylsk, some 20 miles inside Russian territory. Bodies could be seen in the back of some trucks.

About three days after the incursion began, a Ukrainian strike destroyed an apparent munitions depot at Russia’s Lipetsk military airfield in the neighboring region.

Whether or not the strike was directly related to the ground advance, “Ukraine’s Kursk campaign de facto benefits,” said George Barros, an analyst with the Washington-based Institute for the Study of War.

A haphazard evacuation

For Russians near the border, the incursion arrived with loud booms. Roman, 49, a government worker who insisted on anonymity because he feared repercussions for speaking to a Western news outlet, said shelling woke him at 3:30 a.m. in his village outside Sudzha on Aug. 6, the first day of Ukraine’s incursion.

The next day, he and his wife drove to Kursk, the regional capital, because they knew their daughter’s school wouldn’t soon reopen. That night, they returned to evacuate their parents. They drove on side roads with their headlights off, stopping repeatedly to listen for drones.

Roman said people inundated him with requests for help reaching their relatives. He and others said the incursion appeared to have come as such a shock to the authorities that residents had to rely on each other.

A Sudzha resident named Ivan, 34, said in a text exchange Thursday that he was trying to evacuate residents. Later in the day, he wrote that he was in the hospital. His car had been hit by shelling while leaving Sudzha, home to around 6,000 people. And he had learned that the coffee shop where he worked had been damaged in the fighting.

“We’ve all been ditched,” Ivan said, also insisting on anonymity. “People are helping with whatever they can. The government doesn’t care.”

On Monday, the governor of Kursk said more than 100 civilians had been injured and a dozen killed, although the figures could not be independently verified.

The Times reviewed several satellite images captured since Aug. 6 that showed at least two dozen structures were damaged or destroyed in Sudzha and a neighboring village, Goncharovka, including homes, an apartment building, a gas station and support buildings of an arts school.

As the incursion expanded, the city of Kursk — whose name evokes for many Russians the enormous World War II tank battle nearby in which the Soviets stopped the German advance — filled with people fleeing the fighting. They lined up for help at aid centers set up by charity groups, Yan S. Furtsev, 38, an independent political activist in the city, said in an interview.

Nerves were frayed, he said, by shaky cellphone service and incessant air-raid warnings. Buses stopped when the sirens sounded. Those who couldn’t afford taxis were walking to work or relying on strangers for rides.

Whether the incursion would change people’s views on the war was another matter. On state television, the Kremlin played down the significance of the offensive, rather than casting it as a consequence of Russia’s invasion of Ukraine.

“There are a lot of different opinions” about the war, Mr. Furtsev said. “But as for what people think, everyone believes that this is a tragedy.”

Michael Schwirtz, Adam Entous, Dzvinka Pinchuk, Evelina Riabenko, Aric Toler, Christoph Koettl contributed reporting. Axel Boada contributed video production.

Ukraine pressed ahead with its assault inside Russian territory on Tuesday, a week into the biggest foreign incursion into the country since World War II.

While Russian military officials on Tuesday insisted that the situation was under control, Aleksei Smirnov, the acting governor of Russia’s Kursk region, where Ukraine mounted its incursion, warned that “the crisis has not yet been overcome.” And President Volodymyr Zelensky of Ukraine said Tuesday on X that “our forces continue to advance in the Kursk region.”

Col. Roman Kostenko, a member of Ukraine’s Parliament serving in the country’s military, told a local news outlet that the “advance is ongoing.”

The cross-border attack caught Russia by surprise and signified a shift in tactics for Kyiv, more than two years after Moscow’s troops poured across Ukraine’s border in a full-scale invasion.

The rapid advance by Ukrainian forces has been an embarrassment for the Kremlin and aims to alter the narrative of the war at a time when Kyiv’s forces are stretched thin on the front lines of their own country.

Here’s what to know about Ukraine’s cross-border operation in Russia.

What happened?

Ukrainian troops and armored vehicles stormed into the Kursk region of western Russia the morning of Aug. 6, punching through border defenses and seizing several settlements in heavy fighting that left a trail of death and ruin.

The assault opened a new front in the 30-month war and did not just catch Russia off guard: Some Ukrainian soldiers and U.S. officials also said they lacked advance notice.

Russia’s top general estimated that Ukraine had deployed 1,000 soldiers for the incursion, while U.S. officials said Ukraine had sent several thousand. Military analysts have said the attack involved elements of at least four brigades in a rare example of a successful operation involving support from artillery, air defenses and electronic warfare. That translated into quick advances on the ground.

How far into Russia have Ukrainian troops advanced?

Ukrainian forces advanced several miles into Russia within the first 24 hours of the incursion.

By Monday, Mr. Smirnov said that 28 towns and villages were under Ukrainian control. Ukrainian troops had pushed seven miles into Russian territory along a 25-mile front, he said, adding that 12 civilians had died in the fighting.

His claims could not be independently verified, though the description of the extent of Ukraine’s advance was roughly in line with analysts’ estimates.

The head of Ukraine’s armed forces, Gen. Oleksandr Syrsky, on Monday claimed Kyiv had control of “about 1,000 square kilometers,” or just under 400 square miles. Mr. Zelensky said Tuesday on X that “74 communities are under Ukrainian control,” though that could not be independently verified.

Why is this significant?

Kyiv has regularly bombarded Russian oil refineries and airfields with a fleet of homemade drones since Moscow’s full-scale invasion began. It has also helped stage two other ground attacks. Those, however, were smaller forays into Russia by Russian exile groups backed by the Ukrainian Army and ended in quick retreats.

Until last week, Ukrainian forces had not counterattacked into Russia. The gains in Kursk are the quickest for Ukrainian forces since they reclaimed the Kherson region of their own country in November 2022.

How has the Kremlin responded?

As Ukrainian forces pushed deeper into Russia, Moscow scrambled to shore up its defenses and President Vladimir V. Putin convened his security services to coordinate a response.

The Russian military said it was sending more troops and armored vehicles to try to repel the attack, with Russian television broadcasting images of columns of military trucks. Russia has begun to withdraw small numbers of troops from Ukraine to try to help repel the Ukrainian incursion, a U.S. official said on Tuesday without describing how many Russian troops were involved or what impact the reinforcements might have.

While the efforts appear to have helped stall further advances by Ukrainian troops, Kyiv’s forces are holding ground a week into the incursion. They claimed on Saturday to have captured a small village in the neighboring Belgorod region, and analysts say their forces control most of the Kursk town of Sudzha, about six miles from the border.

Russian officials and the state news media have repeatedly claimed to have the situation under control — most recently on Tuesday — only to then lose more ground.

“The operation to neutralize” Ukrainian units, Russia’s Ministry of Defense said on Tuesday, “is in progress.”

And what about Putin?

The incursion has embarrassed Mr. Putin and his military establishment, prompting questions about Russia’s level of preparedness.

Underscoring how the surprise attack rattled the Kremlin, Mr. Putin lashed out at the West in a tense televised meeting with his top officials on Monday.

“The West is fighting us with the hands of the Ukrainians,” he said, repeating his frequent depiction of the war, which he started, as a proxy campaign against Russia by the West. “The enemy will certainly get the response he deserves, and all our goals, without doubt, will be accomplished.”

Mr. Putin directed his military to push out Ukraine’s troops and to work with the border guard service to “ensure the reliable protection of the state border” — an acknowledgment that Russia had failed in that regard.

What has Ukraine said?

It took days for Ukraine to publicly acknowledge the cross-border operation, with the military staying silent in the face of accusations and statements from Russian officials.

Mr. Zelensky’s most explicit reference to the Kursk region incursion came only on Monday night, when he said that Russia had launched attacks from the area.

“Therefore, our operations are purely a security matter for Ukraine,” he said in his nightly address. But he also hinted at another rationale, adding: “Russia brought war to others, and now it’s coming home.”

What is the goal of Ukraine’s incursion?

Analysts say that Ukraine’s offensive most likely has two main aims: Draw Russian forces from the front lines in eastern Ukraine and seize territory that could serve as a bargaining chip in future peace talks.

The operation could also offer a much-needed morale boost for Ukrainians, whose forces have been losing ground to Russian troops for months.

But military analysts have questioned whether Kyiv’s cross-border assault is worth the risk, given that Ukrainian forces are already stretched on the front lines of their own country, including suffering from shortages of troops and ammunition.

How is it affecting the fight inside Ukraine?

Russian forces have been pummeling Ukrainian forces in the east even as Moscow races to respond to the incursion into the Kursk region, according to Ukrainian military officials.

And there is little indication so far that Russia is redirecting frontline forces from eastern Ukraine. Instead of pulling those brigades, Russia appeared to be redeploying lower-level units to the Kursk region, according to a briefing on Sunday by the Institute for the Study of War, a U.S.-based research organization.

While Kyiv’s allies have in the past been wary that Ukrainian incursions in Russia could escalate the war, the United States has suggested that the assault in the Kursk region does not violate American guidance.

However, senior American officials have said privately that they understood Kyiv’s need to change the optics and the narrative of the war, but that they were skeptical Ukraine could hold the territory long enough to force Russia to divert significant forces from the front lines in eastern and southern Ukraine.

What happens next?

Heorhii Tykhyi, a spokesman for Ukraine’s Foreign Ministry, told local news outlets on Tuesday that the country was “not interested in taking territory in Kursk region,” echoing Mr. Zelensky in saying the incursion was aimed at protecting its own citizens.

But it still remains unclear whether Ukraine will try to solidify control over the land it has captured or be forced to retreat.

Russian officials have warned that the incursion could expand. The authorities in the Belgorod region have said they are evacuating a district and Mr. Putin, in his televised meeting, told the governor of a third border region — Bryansk — that it appeared “relatively calm” for now but “this doesn’t mean that the same situation will remain tomorrow.”

On Tuesday, a spokesman for Russia’s emergencies ministry, Artyom Sharov, said more than 2,000 people had left or been evacuated from “borderline districts” in the Kursk region over the past 24 hours, the state news agency Tass reported.

Eric Schmitt contributed reporting.

British counterterrorism police charged seven people with violent disorder on Tuesday, after a group of pro-Palestinian demonstrators forced their way into a building owned by an Israeli defense firm in southwest England.

Seven people ages 20 to 51 were charged with criminal damage and violent disorder, the police said in a statement. One man, age 22, was also charged with assault.

The Crown Prosecution Service, the public prosecutor for England and Wales, said it would argue in a court hearing on Tuesday “that these offenses have a terrorist connection.”

The seven individuals are accused of taking part in a raid in the early hours of Aug. 6 that targeted Elbit, an Israeli defense firm whose British subsidiaries employ around 700 people across 16 sites.

Activists from Palestine Action, a protest movement that aims to disrupt Israeli arms manufacturing in Britain, broke into Elbit Systems U.K.’s research and development site, known as Horizon, last week.

The group used a van to drive through a fence, police said in a statement. Once inside the building in Filton, near Bristol, the group smashed equipment and damaged property. The police said they found axes, sledgehammers and homemade weapons on the scene. Two police officers were assaulted with a sledgehammer, the statement said, and one of them was taken to a hospital for treatment.

More than a dozen people were in the vehicle, but most fled the scene, the police said. Those who were arrested were held under Britain’s counterterrorism laws, which allow police to detain suspects for up to 14 days without charge.

Two other people remain in custody while detectives continue to question them. The investigation, which is still ongoing, is being handled by Britain’s Counter Terrorism Policing unit.

In a statement, Amnesty International, the human rights group, questioned the use of terrorist legislation in the case, and said it had longstanding concerns about such laws being used to “circumvent normal legal protections and to pursue charges that are not commensurate with the facts of a case.”

“The Crown Prosecution Service’s reference to these alleged offenses having a ‘terrorist connection’ is troubling,” said Tom Southerden, Amnesty’s U.K. law and human rights director. He added, “Ordinary criminal offenses can be investigated and prosecuted using ordinary criminal procedures, a process that helps ensure that the rights of those accused are properly protected.”

Before the charges were announced, Palestine Action said in a statement that the attack on Elbit’s site was “to prevent its manufacture of weapons for genocide” and that it wanted to undermine the company’s “profiteering from Israel’s daily massacres.”

The activist group accused the police of launching a “smear campaign” against the seven detained people in claiming they had used violence against police officers and security guards. “The activists are unable to respond to these claims, and unable to describe for public record the force used against them by police and private security,” the statement said.

Palestine Action, which was founded in 2020, has repeatedly targeted Elbit’s drone and surveillance manufacturing sites by vandalizing property, spray-painting slogans and occupying a rooftop.

Elbit said that the Horizon facility did not supply any weapons or technology to the Israeli military or its ministry of defense.

“We provide critical support and advanced technology to the British Armed Forces from our Horizon site,” the group said in a statement.

The weapons manufacturer opened the site in July last year, producing technology for the British Armed Forces and other NATO countries, it said in a statement at the time.

Rawan Yaghi contributed reporting.

The Tanzanian police said on Tuesday they had arrested more than 500 people, including top opposition leaders, as they planned to attend a youth rally, a stunning development in the East African nation where a pathbreaking female president had once promised to restore political freedoms.

Some 520 people were arrested across the country ahead of a Monday rally in the southwestern city of Mbeya, Awadh J. Haji, the police commissioner for operations and training, said in a statement. The police, he said, also seized 25 vehicles that had been transporting people going to the rally and officials from different regions in the country.

The rally was organized by the opposition Chadema party, which said it wanted to mark International Youth Day. But the police banned the gathering before it was underway, and accused party members of making statements that showed their intention to carry out anti-government protests similar to those that swept across neighboring Kenya in recent months.

“Their goal is not to celebrate International Youth Day, but to initiate and commit violence to cause disruption of peace in the country,” Mr. Haji said.

The latest crackdown does not augur well for Tanzania, whose president promised to oversee a more open nation after coming to power in 2021. The country’s first female leader, President Samia Suluhu Hassan, reversed some of the measures put in place by her populist predecessor, including by lifting a yearslong ban on political rallies, easing restrictions on the press and allowing pregnant girls to attend school.

Tanzania was one of three African nations that Vice President Kamala Harris visited last year in her efforts to bolster democratic governance and women’s empowerment in the continent.

But since then, Ms. Hassan’s government has been accused of cracking down on protests against a port management deal, forcibly evicting Maasai communities from their land, suspending news media outlets and arresting journalists — issues that activists say are alarming as the country prepares for local elections in December and a general election next year.

Ms. Hassan has also been criticized for delaying wider reforms, including a review of the country’s Constitution, which grants vast powers to the executive branch and was adopted in 1977, when the country was still a one-party state.

Ms. Hassan’s office did not immediately respond to a request for comment.

The planned youth rally in Tanzania comes as anti-government protests have gripped African countries, including Kenya, Nigeria and Uganda. Demonstrators have focused their ire on government officials, whom they accuse of corruption and overseeing bad economic policies.

In Tanzania, among those arrested was Freeman Mbowe, the chairman of the Chadema party, and his deputy in the mainland, Tundu Lissu. Mr. Mbowe was released from prison in 2022 after charges against him related to terrorism were dropped.

Over the years, Mr. Lissu has become a key detractor of the governing Chama Cha Mapinduzi party — or Party of the Revolution — which has ruled the country since it declared independence. In 2017, he survived an assassination attempt and left the country, but he returned to run for president in the 2020 elections. Facing harassment and intimidation after the bloody and contentious vote, Mr. Lissu again left the country. He returned last year, encouraged by Ms. Hassan’s decision to lift a ban on political rallies, he said.

Mr. Lissu was arrested in Mbeya on Sunday as he and other party members were gathering in the city for the rally. He, Mr. Mbowe and other top officials were released on Tuesday after posting bail, according to a statement from the party posted on social media. The party said its office in Mbeya was “surrounded by the police and they are not allowing people to enter” them.

The latest clampdown has drawn criticism from rights groups who have called on Ms. Hassan to stop them. As elections near, the mass arrests of government opponents were “a deeply worrying sign” for the country, Sarah Jackson, Amnesty International’s deputy regional director for East and Southern Africa, said in an emailed statement.

On Tuesday, the police said they will closely monitor any planned protests or gatherings and will decisively deal with anyone who they say breaches the law.

“The police force continues to closely monitor various information related to plans to break the peace,” Mr. Haji said. “Whoever is identified will be dealt with strictly according to the law, regardless of their rank, position or ideology.”

The head of a panel that ruled that the American gymnast Jordan Chiles had to give up her Olympic bronze medal in favor of a Romanian athlete has represented Romania for almost a decade in arbitration cases, documents show.

The three members of a special tribunal convened for the Olympics by the Court of Arbitration for Sport after Romania lodged a complaint ruled that a successful appeal made by Chiles’s coach over the points awarded to her in the floor exercise competition was initiated four seconds late. The Romanian athlete, Ana Barbosu, was awarded the bronze medal as a result of the panel’s decision, and Chiles was dropped to fifth place.

The result left Chiles brokenhearted: It took away her only individual medal at the Games, and means her appearance on the podium — the first all-Black medals stand at a gymnastics event at the Olympics — is now left with an asterisk. Chiles posted four broken heart emojis on a black background on social media on Saturday after the decision was announced, and later said she was stepping away from social media altogether amid a torrent of racial abuse.

The decision to reallocate the medals in the floor exercise outraged U.S. Olympic and gymnastics officials, who have threatened to take their fight to the Swiss courts. The revelation that Hamid G. Gharavi chaired the panel that resolved the dispute in favor of a Romanian athlete despite having a long relationship with Romania’s government is sure to inflame the case further.

Very little is known about the deliberation and how the panel reached its verdict, with the court publishing just a one-page statement confirming the decisions it made. A detailed document outlining the full reasoning behind the outcome will eventually be sent to all the parties involved.

U.S.A. Gymnastics said on Monday it had been notified by the court that under its rules, the decision cannot be reconsidered “even when conclusive new evidence is presented.”

The gymnastics federation said it would continue to pursue “every possible avenue” for an appeal, including before the Swiss Federal Tribunal. That body, the only one that can hear an appeal against a decision by CAS, the sports court, only considers breaches of process and not new evidence related to the case itself.

In 2021, the Swiss court famously requested a new hearing for a doping case involving a top Chinese swimmer, whose lawyers successfully presented evidence that the chair of the tribunal may have had an anti-Chinese bias based on his social media posts.

Under the court’s rules, panel members, including the chair, must complete a conflict of interest form before reviewing each case that lists three possible outcomes.

The first and third are explicit, revealing no conflict or a conflict so significant that they would require their recusing themselves from a case. The second is more nuanced, allowing arbitrators to reveal potential conflicts but giving them a chance to explain why the potential conflict should not prevent them from hearing a case.

Details first published by The International Institute for Conflict Resolution and Prevention, a nonprofit organization, show that Mr. Gharavi, the presiding arbitrator in the hearing and a lawyer based in France, is currently serving as legal counsel to Romania in disputes at the World Bank’s International Centre for the Settlement of Investment Disputes. Mr. Gharavi’s work on behalf of Romania dates back almost a decade.

Under the sports court’s rules, arbitrators are required to complete conflict of interest declarations before every hearing.

“The issue is whether an Olympic arbitrator who currently represents a country on the global stage can decide a case involving a gymnast of that country, in an unbiased manner,” three arbitration experts wrote in an opinion published on the institute for conflict resolution’s website. “Is it realistic to expect such arbitrator can decide against the interests of that country or of that country’s gymnast, who in this case is represented by the Federation of Romanian Gymnasts?”

Mr. Gharavi said he could not comment on anything related to the case and suggested all such inquires be directed to CAS, which is charged with serving as the final arbiter on global sports disputes. The court said in an email that Mr. Gharavi had disclosed his work with Romania in writing and that none of the parties involved in the hearing had objected to his appointment as the panel’s chair.

“In accordance with the guidelines on conflicts of interest issued by the International Bar Association (IBA), CAS has no reason to remove an arbitrator making such disclosure if the parties do not object to his/her appointment,” the court said in its statement.

Katherine Simpson, an international arbitrator and one of the authors of the opinion piece that first disclosed Mr. Gharavi’s work for Romania, said that even if none of the parties objected, his work on behalf of Romania was significant and meant he would automatically have had to recuse himself under the IBA’s so-called red list of non-waivable activities.

“I don’t understand — especially given the visibility of the case — why he was proposed for this case and why he did not refuse the case when it was offered,” said Ms. Simpson, who is not connected to the case.

Mr. Gharavi won a case on behalf of Romania as recently as June, and his biography on his firm’s website lists Romania as a regular client.

The court later issued a separate statement confirming that it could not reopen the case. It said all the parties involved had had what it described as “ample opportunities” to present their arguments and objections. New evidence, if found, could be used to ask the Swiss Federal Tribunal to order the case be reopened and the CAS “would also reopen the case spontaneously if all parties agree.”

Such an outcome, however, is extremely rare.

CAS rulings are almost always the final word in such cases, with the Swiss tribunal typically rejecting most appeals of the rulings. But the Chiles case is likely to bring new scrutiny about how such matters are handled in international sports. Cases are almost always heard behind closed doors, with the full rationales for decisions sometimes limited to just the parties involved in cases, leaving sports fans and athletes unsure about exactly why certain outcomes have been reached.