Olha Predchenko held hands with her 85-year-old mother as they looked at the makeshift memorial on the grass in central Kyiv, each blue and yellow flag marked with the name of a soldier who had died fighting in the war with Russia.

They come here often to Maidan Square, to spend time thinking about the dead and the war. Ms. Predchenko said she dreamed of something heavy falling on the Kremlin. But she also hoped for a peace deal soon.

“Better a bad peace than a good war,” added Ms. Predchenko, 61.

Increasingly frustrated, more Ukrainians appear to be opening up to the idea of a negotiated peace, even as they remain vague about what that means.

Most Ukrainians still oppose ceding any territory to Russia, not even the Crimean peninsula that was seized by Russia 10 years ago, polls show. But those polls and recent remarks by the country’s leaders also highlight a palpable shift in the conversation around peace talks — from a no-deal-not-ever to a maybe-compromise-at-some-point.

In mid-July, a survey by the Ukrainian independent media outlet ZN.UA found that about 44 percent of Ukrainian civilians favored starting official talks with Russia. On July 23, the Kyiv International Institute of Sociology released a poll showing that nearly a third of Ukrainians would agree to cede some territory to Russia to end the war. That’s more than three times as many as the year before.

Nadia Ivashchenko, 28, a railway signal operator from the central Kirovohrad region, said she couldn’t describe a good peace settlement. But her husband has been fighting in the army since Russia invaded in February 2022, and the couple has a 5-year-old son who hasn’t seen his father in years.

“So many people died, and what for?” Ms. Ivashchenko said. “But I want everything to be finished, at least somehow, because I have a son, and I don’t want him to grow up in such a wartime as now.”

In Ukraine, the third year of the war is grueling: The Russians are inching forward every day, and Ukraine has been unable to mount a successful counteroffensive since 2022. The country has been beset by frequent power outages and a growing death toll.

Ongoing support from the West seems unpredictable, especially if Donald J. Trump regains the White House in November. Germany will cut military aid for Ukraine in half if its proposed budget for 2025 is adopted; that is seen as a bellwether for Western commitment, especially after the six-month delay in the United States for a military-aid package delivered this spring.

International pressure is building on Ukraine and Russia to come to some kind of agreement, although experts agree neither side is ready. The barriers to any settlement are huge: Russia occupies about 18 percent of Ukrainian territory, including Crimea, according to DeepState, an analytical group with close ties to Ukraine’s army.

In June, President Vladimir Putin said he would order a cease-fire and enter negotiations with Ukraine only if Kyiv withdrew from the regions that Moscow has claimed — but does not yet completely control — and dropped aspirations to join NATO. Ukraine dismissed the proposal as a demand for capitulation; President Volodymyr Zelensky has said he wants Ukraine to return to its 1991 borders and gain a NATO berth.

Russia was not invited to Switzerland in June for the first international peace summit, a 92-country gathering meant to promote Ukraine’s vision for how the war should end. Since then, Ukraine has publicly signaled that Russia should come to the next one, and Mr. Zelensky, in an interview with the BBC, expressed hope for a diplomatic solution.

Ukraine’s foreign minister was in Beijing this month expressing a willingness to have China play a more central role in peace negotiations, and on Wednesday Ukraine invited China’s top diplomat to visit Kyiv.

Russia has so far been noncommittal about participating in a second peace summit. But the Kremlin has also signaled in recent weeks that it could enter negotiations even if Kyiv doesn’t fulfill Mr. Putin’s June demands. Regardless, many Western officials and analysts question whether Mr. Putin is ready to negotiate anything other than a peace deal on his terms.

A key adviser to Mr. Zelensky last week said making a deal now with Mr. Putin was akin to signing “a deal with the devil.” And while the Kyiv Institute poll showed a threefold increase in people willing to give up land for peace, it also found that 55 percent of Ukrainians oppose any territorial concessions whatsoever.

Kateryna Predchenko, Olha’s 85-year-old mother, chastised her daughter for suggesting a deal and thought Ukrainian soldiers should keep fighting.

“It’s not just Ukraine, they protect the whole world,” she said. “Why doesn’t the world want to understand this? We need everyone to rise up against this Russian idiot.”

In the south, one of the regions most affected by the war, the change in attitude over the past year was striking, the Kyiv Institute’s poll showed. More than half of the respondents said they either supported ceding some territory or weren’t quite sure. Only 46 percent said they opposed any concessions. A year ago, 86 percent in this region — encompassing Dnipropetrovsk, Zaporizhzhia, Mykolaiv, Kherson and Odesa — said they opposed giving any territory to Russia.

Mykola, 33, a resident of Odesa, who didn’t want his last name used because he was avoiding the military draft, said he could see ceding the Crimean peninsula, already in Russia’s control, or the area near the city of Luhansk in eastern Donbas as part of a deal. But he added: “As a person who’s sitting home and not fighting on the battlefield, I don’t feel I have any moral right to say how this agreement should look.”

Freezing the lines of battle would leave those in occupied areas, which include the relatives of many Ukrainians, in Russian control indefinitely. And the areas Ukraine has liberated are grim, destroyed by Russian strikes and rife with allegations of human rights abuses.

The sociology institute’s survey did not identify how large concessions should be, whether territory should be officially conceded or whether it should be controlled temporarily by Russia in a less formal way.

“It’s just in general, what’s your emotions?” said Anton Grushetskyi, the institute’s executive director. “And surely, more and more people are ready. And the key reason is the failed expectations from the last year, because lots of people had more hopes.”

He added that many Ukrainians had seen those hopes dashed, particularly because of the delay in U.S. military aid.

For some Ukrainians, their desired deal sounds more like a pipe dream.

“I’d like Russia to go home, stop interfering in our country and deal with their internal problems,” said Oleksandr Melnyk, 26, a car mechanic in the southeastern city of Kryvyi Rih. He said he has submitted his papers to serve in the army. “I’d like them to stop their aggression, pay for the damage, and return all our prisoners and children.”

Many in Ukraine said they were nervous about what the re-election of Mr. Trump might mean. The former president has said he plans to bring a swift end to the war, although he hasn’t specified how. Ukrainians worry that he would cut America’s support or push to allow Russia to keep the territory it now occupies.

Mr. Trump’s inner circle is filled with Ukraine war skeptics, including JD Vance, his pick for vice president, who once said: “I don’t really care what happens to Ukraine one way or another.”

But other Ukrainians said that Mr. Trump would at least give Ukraine an answer.

“If Trump comes to power, everything will be clear,” said Natalia Fomenko, 47, who lives in Irpin, one of the Kyiv suburbs ravaged early in the war by the Russians. “Either he will provide Ukraine with weapons, or we will have to agree to negotiate.”

Some Ukrainians on the front lines also said they were skeptical that Russia would actually honor the terms of a peace deal.

“I’d rather believe in the chastity of a prostitute,” said Oleksandr Tsebrii, a soldier of the 58th motorized brigade, in a Facebook video posted on July 15, shortly after Mr. Zelensky publicly suggested Russia could come to the next peace summit. He added: “The only formula for our security and the existence of Ukraine is our resistance.”

Last week, he was killed in heavy fighting in the eastern region of Donetsk.

Anton Troianovski, Andrew Kramer and Dzvinka Pinchuk contributed reporting.

Sudan’s army said two drone strikes hit an army base in the country’s east on Wednesday after a graduation ceremony attended by the country’s de facto leader, Gen. Abdel Fattah al-Burhan, who has been locked in a civil war for over a year with a rival military general.

At least five people were killed and several others injured in the attack in the town of Gebeit, the army said, which has been held by the army and is about 50 miles from its wartime capital of Port Sudan. The Sudanese army spokesman, Nabil Abdallah, told the BBC that General al-Burhan had survived an assassination attempt, and blamed it on the Rapid Support Forces, the paramilitary group that has been battling the army for power for 15 months.

A military spokesman could not be reached for comment. In statements posted on social media, the military did not say whether General al-Burhan had been hurt or where he was during the attack. But it posted videos showing him interacting with the soldiers and members of the public before and after the graduation ceremony.

No group has claimed responsibility for the strikes. The paramilitary group’s media office did not immediately respond to a request for comment.

The war between General al-Burhan and his rival, Lt. Gen. Mohamed Hamdan, who leads the Rapid Support Forces, has devastated Sudan, one of Africa’s largest nations. More than 18,000 people have been killed, according to an estimate from the Armed Conflict Location and Event Data Project, though aid workers estimate the death toll to be higher.

At least 10 million people have been driven from their homes, according to the United Nations, while more than half the country’s 48 million people face hunger, and hundreds of thousands of others are facing a looming famine.

The army and the paramilitary group have both used drones in the war, which are sometimes supplied by close foreign allies such as Iran or the United Arab Emirates, according to Western and Sudanese officials.

The paramilitary group, which has dominated the capital, Khartoum, and the western region of Darfur, has in recent weeks been ramping up its attacks on areas controlled by the army in the east. The paramilitary group has also recently clashed with the army in El Fasher, the capital of North Darfur, and in the southeastern state of Sennar.

The two military leaders were once allies who brutally cracked down on Sudan’s pro-democracy forces after a popular revolt forced out the country’s longtime dictator, Omar Hassan al-Bashir. But they fell out over who should hold supreme power in the country and how swiftly their forces should merge into a single army.

The reported drone attacks on the base come just two weeks before mediation talks to end the war, hosted by the United States, were set to begin in Switzerland. The U.S. secretary of state, Antony J. Blinken, said in a statement this month that Saudi Arabia will co-host the talks, which will include the African Union, Egypt, the United Arab Emirates, and the United Nations as observers.

The paramilitary force’s leader, General Hamdan, said his group will participate in the talks. On Tuesday, Sudan’s foreign ministry, which is allied with the army, signaled it was ready to join the talks in Geneva on Aug. 14. but said the paramilitary should stop its attacks and open humanitarian corridors.

The army, however, has also been accused of thwarting the flow of food aid, especially to the Darfur region in the west, by preventing United Nations trucks from passing through a crucial border checkpoint. The army says it is necessary to stop the flow of weapons.

The war in Sudan has become one of the world’s most urgent, and ignored, humanitarian emergencies. The country’s health care system has been all but decimated, disrupting treatment for millions. Disease outbreaks have risen, with aid groups saying hundreds have died from malaria, dengue, measles and other illnesses.

Schools and universities have been shuttered in a nation that once drew many foreign students. Looting has been widespread, with banks, private homes and government institutions burned and robbed.

It had already been clear for months that Venezuela’s presidential election on Sunday, would not be free or fair, as the government jailed opposition leaders or disqualified them from running for office.

But as the day progressed it became all the more evident just how flawed the country’s democratic process had become and why the victory claim by the country’s autocratic leader, President Nicolás Maduro, has provoked such fury.

Voter intimidation

Across the country citizens, local reporters and journalists for The New York Times observed instances of voter intimidation.

In the early morning about 15 men in unmarked black jackets temporarily blocked access to one voting center in the capital, Caracas, a Times journalist observed. One volunteer vote monitor was punched.

The crowd eventually started demanding the right to vote and the long line started moving inside, more than an hour and a half after voting was officially supposed to start.

In the eastern city of Maturín, woman was hit by a bullet when men on motorcycles drove by a line of people waiting to vote, according to a former lawmaker, María Gabriela Hernández, who was at the scene.

And in another polling place in the northern city of Cumaná, roughly 50 armed police officers and national guardsmen formed a long line outside, wearing helmets and body armor, in what appeared to be a show of power to anyone considering voting against the government.

In the nearby city of Carúpano, citizens and local journalists said that government security forces had tried to remove a vote monitor allied with the opposition and replace the person with a different monitor who had not been authorized by the country’s electoral authority.

Changing some voting stations

About 17,000 Venezuelans saw their voting stations changed at the last minute according to Carlos Medina, who helps direct the Venezuelan Electoral Observatory, an independent group.

That was the case for many voters in Maracaibo, Venezuela’s second largest city.

Sonia Gómez, 65, said she had checked the election council website on Saturday to verify her polling station. But when she arrived on Sunday, election workers told her she was registered somewhere else.

“They moved us older people because they know we don’t have that much energy,” she said, “but I’m going to look for someone to take me to vote.”

Five people in Cumaná said a new, unofficial voting station had been installed in a community center. A journalist working for The New York Times who tried to enter the site was stopped by government supporters.

Keeping other polling places open late

Some stations stayed open beyond the scheduled end of the vote, giving members of Mr. Maduro’s party a chance to round up voters who had yet to cast their ballots.

“The opposition vote is more spontaneous, it arrives by its own means,” Mr. Medina said. “On the other hand, the pro-government vote has behind it a machinery that mobilizes the vote.”

“So they left the centers open longer,’’ he added, “which allows the machinery to have more time to continue doing the work of searching and mobilizing the vote in favor of the ruling party.”

Withholding paper tallies

There are two vote counts in Venezuela, a digital tally received by the country’s election authority — which is led by an ally of Mr. Maduro — and a paper count printed by each voting machine at polling places.

The opposition invested heavily in an effort to have supporters present at each voting station to obtain a physical printout of the voting tally from every voting machine after the polls closed.

That access is required by Venezuelan election law, and the paper counts are typically the way that everyday citizens can verify that the digital count is correct.

But officials at some polling places refused to release the printouts to election monitors.

This was the case at one of the largest voting stations in Caracas, the Rafael Napoleon Baute school in Petare, where about 15,000 people were registered to vote.

In Maracaibo, local leaders said they had not been able to get the paper counts for all the voting centers in the region. At one school, Colegio Gonzaga, citizens protested outside, calling on the electoral officials to turn over the voting receipts.

Without all the paper counts, the country was left without a way to verify the result announced by the ruling party.

Not publishing a full vote count

Shortly after midnight early Monday morning the country’s electoral authority announced that Mr. Maduro had received 51.2 percent of the vote, while the main opposition candidate, Edmundo González, had received 44.2 percent, with 80 percent of voting stations counted.

But the government did not release a full vote count, and its figures did not appear to match statistical estimates based on partial counts gathered by opposition poll watchers and other data that showed the president losing by a wide margin. As of Wednesday, the government had still not provided a full vote count.

The results were immediately called into question by the opposition and by the United States and other countries around the world, including several leftist Latin American governments.

“One of the main guarantees of our automated voting system is accountability, and accountability requires that the election results be published table by table to be able to verify the result,” said Mr. Medina. “Otherwise it is an act of faith, to believe in one number or another.”

If the country’s electoral authority does not reveal the results for every voting machine,’’ he added, “it would be implicitly saying that it cannot support the numbers.”

She was boxing for money. Even at 13 years old, she knew that.

Why else, said Janjaem Suwannapheng, would she commit to a sport in which a boy smashed her nose in, back when she was shorter than the stalks of rice in the fields near home?

“Anyone who becomes a boxer does it because they come from a poor background,” she said. “It hurts, it’s tiring, it’s exhausting.”

Of course, Janjaem is really good at boxing. She was the first girl to train at her local gym in Thailand’s rural northeast. She loves the sport now, she said. At last year’s world championships, she won a silver medal in her welterweight division (66 kg, about 145 pounds). At the Paris Olympics, she is into the round of 16 with a bye.

Even if she goes no further, Janjaem said, boxing has already saved her. Now 24, she has bought land and gold for her parents and a pickup truck for herself. She scored an athletic scholarship to a university. Her older brother, by contrast, left school at 15 to work with their father, a truck driver.

Boxing is a national passion in Thailand, where the confluence of hardscrabble living and a fondness for illegal gambling — on anything from cockfighting and buffalo racing to a fin-snapping standoff between Siamese fighting fish — has made the sport tremendously lucrative. The local variety, muay Thai, or Thai boxing, relies on lightning strikes with legs, knees, elbows and fists first honed by ancient warriors dedicated to the “way of the eight limbs.”

Muay Thai boxers wear no protective gear on their heads. In 2018, a 13-year-old fighter died of a brain hemorrhage after he was knocked out in a bout. Legislators talked about tightening regulations for minors. Not much happened. The sport continues to gird the illegal gambling economy.

In a country with the highest income inequality in East Asia and the Pacific, according to the World Bank, boxing allows young people to vault fast from subsistence farming to the climate-controlled privilege of Bangkok. By winning bouts, Thai prisoners can earn early release, as one flyweight boxer who competed in the 2008 Beijing Olympics did after his sentence for robbery was commuted.

Thailand’s impoverished northeast, known as Isaan, cultivates the majority of the country’s boxers. The region’s labor force is scattered around the country and the world because there aren’t enough jobs back home. Last October, about two dozen Isaan workers were kidnapped from Israeli farms near Gaza; more than 40 Thai farmhands have been killed by Hamas.

“From working in the fields, from working in the sun, we get the fighting spirit,” said Thananya Somnuek, who started boxing as a young teenager in Isaan.

Thananya won a national championship at 16 and later a gold medal at the Youth Olympic Games. Her nickname in Thai is Butter, because her mother had a premonition that her daughter would one day go to a foreign country where people ate such foreign ingredients. One of Thananya’s boxing squad teammates, another Isaan native, is nicknamed Cream. Both Butter and Cream made it to Paris.

Officially, children in Thailand can enter the muay Thai ring at age 10. If they are healthy, they can box for money every 21 days. But in Isaan, locals say, standards are more lax. As long as farmhands aren’t needed for the harvest, children can fight every 10 days.

“The strict rules are made by air-conditioned men sitting in air-conditioned rooms,” said Suthep Saengngoen, as he sat in his family’s sweltering muay Thai gym, rubbing his grandson’s body with a cooling mentholated liniment. His six sons all fought, too.

The family is from Isaan, but the gym is in the outskirts of Bangkok, amid industrial warehouses and scraggly fruit farms. Boxing purses in the Thai capital are at least triple those back home.

Suthep’s grandson, Chaichana Saengngoen, was named a muay Thai rookie of the year in 2023. He’s now 16 and, in addition to his earnings in the ring, receives $1,300 in endorsements every month.

“I started boxing because my grandfather forced me to,” Chaichana said. He was 7 when he began.

“I do like it now,” he added.

The children at the gym train from five to seven in the morning, before going to school. Then they return for afternoon practice until the mosquitoes start swarming at dusk. That’s not counting 10 kilometers (6.2 miles) of running twice a day to build stamina. By the end of the day, their young arms shiver from smacking the bag — and each other — hundreds of times. Hundreds of roundhouse kicks leave their legs quaking, too. Still, they return for more.

Nutthapol Anuphap, 10, has been boxing since he was 3, he said. At 5 years old, he appeared on a local TV talent show. One of his muay Thai videos has nearly 2 million views. His nickname is Fist.

“I’m going to be rich,” he said.

At the Chaiya District Prison in southern Thailand, in a concrete yard flanked by razor wire, a group of inmates heaved, kicked and punched in the 97-degree heat. One lifted a cement-filled bucket with his teeth, strengthening his jaw and neck with each 22-pound (10 kilogram) rep.

Out of the more than 900 inmates at Chaiya, 15 men and five women have qualified for a prison muay Thai program, one of 10 in the country. They train for eight hours a day and receive extra rations of eggs, meat and milk.

“Muay Thai training gives the prisoners resilience,” said Sathika Samsri, the superintendent of Chaiya. “We want to build them into professional boxers or trainers who will not return to prison.”

The fighters can keep their prize money, and prison officials allow them occasional perks such as KFC spicy chicken wings, a local favorite. Successful bouts at local stadiums, which they attend with prison officials in tow, count as good behavior in parole hearings.

Jomyud Sowangchompu, 21, was sentenced to four years in prison for drug dealing and possession. He left school in sixth grade and could only find a job making less than $15 a week during the fruit harvesting season, he said. In a town match in June, he lost in the first round. Still, he earned $55 for fighting, enough to pay for months of prison necessities: soap, toothpaste, laundry detergent, haircuts.

“I don’t have to ask my parents for money,” he said. “It makes me feel like a better man.”

None of the prison boxers said they have any interest in watching the Paris Olympics, even if the wardens were to allow them screen time At the Bangkok muay Thai gym, the children and coaches seemed mystified by the Olympic boxing rule limiting participation to amateurs.

“What’s the point of boxing if you can’t make lots of money?” said Suthep, the gym family patriarch.

Besides, he said, without the kicks, knees and elbows of muay Thai, Olympic boxing seemed like only half a sport.

Demonstrations of muay Thai are taking place on the sidelines of the Paris Games. But the sport, while gaining in popularity overseas, has nowhere near the profile of international boxing. And for all the money to be made — and gambled — in muay Thai, the professional boxing circuit is far more developed. Many Olympic boxers retire and go pro.

Wijan Ponlid began training in muay Thai at age 9, then won flyweight gold at the 2000 Olympics in Sydney. A parade of elephants greeted him upon his return, and he was handed a cushy job as a police officer. Today he’s the coach of the Thai women’s Olympic team. Among his duties: figuring out how to nourish the squad in Paris with their beloved shrimp and chili paste, an Isaan specialty.

“I switched to international boxing because with muay Thai, I got to a point where I was the world champion, but I wanted to be part of a national team with the flag on my chest,” Wijan said.

For Thai women, international boxing offers even more opportunities.

Jutamas Jitpong, the daughter of rubber tappers, started in muay Thai at 9 years old. Within three years, she was a champion, but there were few girls of her caliber with whom to compete. Some muay Thai stadiums, governed by rules loosely affiliated with Buddhism, don’t allow women to enter the ring, much less fight. In three years, she fought three times.

So Jutamas, now 26, switched to boxing. Although women’s boxing became an Olympic sport in 2012, Thailand didn’t send any athletes in the event until four years later.

Jutamas won a flyweight silver at the 2022 world championships and a bronze a year later. She made it to the round of 16 in Paris.

“Maybe people thought, you’re a woman, you really want to box?” Jutamas said. “I want to box. I want to win.”

Israel launched a deadly strike in a densely populated Beirut suburb on Tuesday in retaliation for a rocket attack in the Israeli-controlled Golan Heights that it blamed Hezbollah for and that killed 12 children and teenagers on a soccer field.

The target of the Israeli strike in a southern suburb of Lebanon’s capital was Fuad Shukr, a senior official who serves as a close adviser to Hezbollah’s leader, Hassan Nasrallah, according to three Israeli security officials who spoke on the condition of anonymity to discuss sensitive details.

The Israel Defense Forces later said in a statement that its fighter jets had “eliminated” Mr. Shukr, but there was no confirmation from Hezbollah, the powerful Iran-backed group, and the claim could not be independently verified.

Hezbollah has denied carrying out the attack in the Golan Heights on Saturday. The latest strikes were likely to fuel concerns that Israel’s long-running conflict with the group could escalate into a full-blown war even as Israel wages a military offensive against Hamas in the Gaza Strip after that group led a deadly assault in Israel on Oct. 7.

The attack on Tuesday is believed to be the first time since the war with Hamas began that Israel has targeted Hezbollah in Beirut. In January, an Israeli airstrike in a Beirut suburb killed Saleh al-Arouri, a senior leader of Hamas, which is also backed by Iran.

The strike on Tuesday killed at least three other people — a woman and two children — and wounded at least 74 others, five critically, according to Lebanon’s Ministry of Health. Officials were still searching the rubble for other victims, the ministry said.

Lebanon’s caretaker prime minister, Najib Mikati, condemned the strike, which he said had hit close to one of the country’s largest hospitals. A spokesman for António Guterres, the United Nations secretary general, expressed “grave concern” about the attack.

The strike hit close to Hezbollah’s Shura Council, a central decision-making authority, Lebanon’s state-run news agency reported. Videos and photographs on social media showed smoke rising above buildings as darkness fell over Beirut, home to about 2.4 million people.

Crowds filled the streets after the strike in the neighborhood of Haret Hreik, which is the headquarters of Hezbollah and which was largely destroyed by Israeli airstrikes in 2006 during the last war between the two sides.

Mohamed Awada, 52, a taxi driver who lives in Beirut’s southern suburbs, said he had been opening the door to his house when he “heard something like thunder and then a big explosion.”

“Everybody in the street was yelling and screaming,” he added. “It feels like we are already in a war.”

Hezbollah began firing into northern Israel in what it called a show of solidarity with Hamas after the assault on southern Israel in October. Since then, Israel and Hezbollah have traded thousands of strikes across the Israeli-Lebanese border, wrecking towns, killing hundreds and forcing more than 150,000 people in both countries to flee their homes.

The rocket attack on Saturday hit the Arab Druse village of Majdal Shams in the Golan Heights. The Israeli military said that Hezbollah was the only militant group in the region with the type of rocket used in the strike, the Iranian Falaq-1. U.S. officials said it was a Hezbollah rocket fired from territory the group controls.

On Monday, Prime Minister Benjamin Netanyahu of Israel promised a “severe” response to the rocket attack. But international diplomats have been pressuring Israel to be measured in its response, said one official familiar with the discussions. The United States was among the countries urging restraint, said the official, who spoke on the condition of anonymity to discuss sensitive diplomacy.

Members of Israel’s security establishment also told the cabinet this week that it was not a good time to engage in a major war with Hezbollah, according to two Israeli officials who spoke on the condition of anonymity to discuss internal deliberations.

Biden administration officials have repeatedly said this week that they were working toward a diplomatic solution to the fighting between Israel and Hezbollah. After the Israeli military reported it had struck Beirut on Tuesday, the White House press secretary, Karine Jean-Pierre, told reporters in Washington: “We do not believe that an all-out war is inevitable. We believe that it can still be avoided.”

Ms. Jean-Pierre added that the White House was still confident that a diplomatic solution to the conflict could be negotiated. “We have to continue to be optimistic here,” she said.

Abdallah Bou Habib, Lebanon’s foreign minister, said the United States had asked Lebanon’s government to relay a message to Hezbollah not to retaliate because of fears of a wider escalation. “We prefer no retaliation at all,” he told The New York Times. “But if there is a retaliation, we want it to be less than proportional.”

He added that he was trying to persuade Hezbollah to be restrained in any response.

Mr. Shukr was Hezbollah’s “most senior military commander,” and was responsible for the group’s precision-guided missiles, cruise missiles, anti-ship missiles, long-range rockets and drones, the Israeli military said.

After a senior Hezbollah commander, Mustafa Badreddine, was killed in Syria in 2016, Mr. Shukr assumed some of his responsibilities, said Hanin Ghaddar, an expert on Lebanese affairs and a senior fellow at the Washington Institute for Near East Policy. Ms. Ghaddar said Mr. Shukr had been a powerful military figure within Hezbollah and was responsible for operations in southern Lebanon.

“He’s a very big target,” she said. “He would be the biggest loss for Hezbollah since Oct. 7.”

Mr. Shukr played a major role in the 1983 bombing of a U.S. Marine compound in Beirut that killed 241 American servicemen and wounded 128 others, according to the website of the State Department’s Rewards for Justice program.

The program was offering up to $5 million for information on Mr. Shukr, and the State Department labeled him a “specially designated global terrorist” in 2019, the website read.

Before the strike on Tuesday, Giora Eiland, a retired major general in the Israeli military and former Israeli national security adviser, had predicted that Israel would carry out a limited strike in response to the attack on Majdal Shams.

“Israel cannot begin a total war in Lebanon today without real international support,” he said.

But General Eiland said he was concerned about a scenario in which Iran participated in the retaliation to an Israeli strike against Hezbollah.

“We’re facing terrible dangerous scenarios,” he said. “We have no choice but to be more careful.”

Hours before Israel struck near Beirut, Iran’s new president, Masoud Pezeshkian, was sworn in at a ceremony at the Iranian Parliament in the capital, Tehran. Mr. Pezeshkian beat a hard-line conservative in a July runoff election.

In the front row sat the leaders of regional militias backed by Iran and known as the “axis of resistance”: Hezbollah, Hamas, Palestinian Islamic Jihad and the Houthis.

During the ceremony, some in the audience broke out into chants of “death to America” and “death to Israel,” when Parliament’s speaker, Gen. Mohammad Baqer Ghalibaf, mentioned the war in Gaza and U.S. support of Israel.

“We want a world where Palestinians are free from the clutches of injustice and occupation,” Mr. Pezeshkian said. “And the dreams of no Palestinian child is buried under the rubbles of their home. We can help realize this dream.”

The Iranian Embassy in Beirut “strongly condemned” the attack on Tuesday, calling it “cowardly and criminal,” according to Iranian news media.

Lebanese television channels showed footage of a building collapsed in on itself. Fire trucks and ambulances rushed through Beirut’s streets to the site.

The Lebanese Red Cross said in a statement that a residential building had been struck. The building had more than six floors and was badly damaged. Later Tuesday, the area around it was cordoned off.

The latest exchanges between Israel and Hezbollah come as Palestinians in Gaza have been told by the Israeli military to move to an area that the military has designated as a “humanitarian zone,” and that area keeps shrinking.

In the latest downsizing, the military this weekend ordered the evacuation of two more parts of central Gaza that had been part of the zone. Similar orders have forced more than 200,000 Palestinians to relocate over the past week alone, according to the United Nations.

The Israeli military has said its recent evacuations and operations have targeted a renewed Hamas insurgency, and it has accused the group of launching rockets from the areas that fell under the latest evacuation order.

But the repeated redrawing of the zone’s borders was one more burden among many for Gaza’s 2.2 million people.

Philippe Lazzarini, the head of the U.N. agency that aids Palestinians, said on Sunday that evacuation orders had affected “almost everyone in Gaza.”

The orders bring “more misery, fear and suffering for people who have nothing to do with this war,” Mr. Lazzarini said on social media.

Reporting was contributed by Michael Levenson, Ephrat Livni, Aaron Boxerman, Hiba Yazbek, Lauren Leatherby, Abu Bakr Bashir and Ameera Harouda.

Now that she has mastered it, the uneven bars routine that the gymnast Kaylia Nemour has prepared for the Paris Olympics is a sight to behold: a fluid yet treacherous 30 seconds, so tightly woven with difficulty that it has made her a medal favorite in the event.

When Nemour performed it in competition last month, it produced the highest score recorded on the bars since the Tokyo Olympics. But while she may wow fans in her home country at these Games, she won’t be doing it under the French flag.

Instead, Nemour, 17, is competing for Algeria, the result of a nationality switch last year that followed a protracted dispute with the French gymnastics federation — one that has seen the host nation lose out on perhaps its best chance for a medal on one of the most high-profile stages of the Games.

The conflict that drove a wedge between Nemour and the French federation began with a power struggle over training sites ahead of the Games but has since devolved into accusations of overtraining, caustic exchanges and an 18-month administrative inquiry that concluded last December that the federation was “hounding” Nemour’s home gym in Avoine, a village in western France.

“Kaylia’s dream was to represent her country, France, at the Olympics, like any high-level athlete,” said her mother, Stéphanie Nemour, who is also the president of the gym. “We have distressed gymnasts here who don’t understand why the federation that is supposed to nurture them is acting this way.”

Through a spokeswoman, the federation declined to comment on its dispute with Nemour and her coaches or on her split with the federation.

Nemour’s road to the French national team once looked exceptionally smooth. While many aspiring gymnasts have to move or commute long distances to train for elite careers, the Nemours happened to settle less than a mile from Avoine Beaumont Gymnastique, a gym where Marc and Gina Chirilcenco have coached a steady stream of top gymnasts over the past 30 years.

Her potential was obvious from a young age, according to Marc Chirilcenco. “She has exceptional air awareness, and for a long time, she simply had fun with it,” he said. In 2020 and 2021, while still a junior, Nemour beat her senior peers at several French events. In 2021, she became the national champion in the uneven bars.

Around the same time, the French gymnastics federation announced new training guidelines. Instead of choosing their training location, all Olympic hopefuls would be required to train full-time under the umbrella of the National Institute of Sport, Expertise and Performance either in Vincennes, a suburb of Paris, or in St.-Étienne, in southeastern France.

For the Olympic hopefuls training in Avoine, a small group that included Nemour, the edict was a significant blow. Nemour said that leaving her hometown “wasn’t even an option.”

“I’ve been here pretty much since I was born,” she said. “My home is within walking distance from the gym. I’m really happy with my coaches. Why would I leave?”

A parallel issue added fuel to the fire. In 2021, Nemour was found to have advanced osteochondritis, an inflammation that is often linked to repetitive stress placed on a joint. Nemour’s surgeon opted to perform bone grafts on her knees “to give her the best chance” to return to a high level, Stéphanie Nemour said.

While osteochondritis can be common in gymnasts, and even congenital, the severity of Nemour’s condition led the French gymnastics federation to wonder if it had been caused by overtraining, a charge that had arisen before with athletes working with the Chirilcencos.

Céline Nony, a gymnastics reporter for the French newspaper L’Équipe, said that the couple were known to “push for high difficulty at too young an age.” Chirilcenco disputed the accusation: “We train roughly the same number of hours as other French training centers, and we have no more injuries,” he said.

The two issues — Nemour’s training location and health — soon became conflated. When Nemour got the all-clear from her personal doctors to resume training in March 2022, the federation’s doctor refused to agree.

Chirilcenco soon lost his position as a national coach. The gym was stripped of its status as a state training center — losing funding in the process — and the federation asked the regional authorities to investigate the Chirilcencos and what it charged was their “excessive influence over minor athletes and endangerment of them.” After 47 interviews with gymnasts, parents and staff, the inquiry ultimately cleared the coaches.

The idea of competing for Algeria materialized as a way out of the standoff. Nemour’s father had an Algerian passport because his parents had been born in the country, and Nemour was entitled to one as well. “I wanted a solution, to avoid spending another year without being allowed to compete,” she said.

Algerian gymnastics officials welcomed her. An athlete of Nemour’s caliber had the potential to raise the profile of the sport not just in the country but across Africa, which had never earned a world or Olympic medal in women’s gymnastics.

France didn’t let Nemour go so easily, however. Under international rules, gymnasts must obtain a letter of release from their former federation to compete under a new flag, or face a one-year delay. Only the intervention of the French sports minister last year released her in time to qualify for the 2023 world championships.

There, in October, Nemour won the silver medal on the uneven bars at age 16. She didn’t realize what the result meant for African gymnastics, she said, until she started receiving a deluge of messages and interview requests. “It came as a shock,” she said. “There was so much support from Algeria that I’m really happy to represent the country.”

An Olympic medal would be an ever bigger breakthrough. While the uneven bars offer her most promising chance — she qualified for the apparatus final with the highest score on Sunday — Nemour has also recently emerged as an all-around threat: She is the fourth-ranked gymnast entering the final on Thursday.

For France, which has a respected history in gymnastics but rarely features among medal favorites at the Olympics, the loss of an athlete of her ability is incalculable. “With Kaylia, the French team was at least twice as likely to win a team medal at a home Games, aside from her individual potential,” said Nony, the sports journalist. (In Sunday’s qualification round, France failed to qualify for any women’s final.)

With the ordeal behind her, Nemour said that she felt “no heartache” over competing for another country in Paris.

“The Olympics were a goal I had for myself,” she said. “Whether it’s for France or Algeria, it will still be me, Kaylia, on the floor.”

Almost 40 police officers were injured in the northwestern English town of Southport on Tuesday evening after a day of mourning for children killed in a stabbing attack was disrupted by far-right protesters.

A large group that the police say included supporters of the English Defence League, a far-right extremist organization, began attacking a mosque in Southport on Tuesday evening, according to a statement from the Merseyside Police Service, which covers the region.

Officials said that the targeting of the mosque and the ensuing riot appeared to be linked to online disinformation about the stabbing on Monday, when an attacker killed three children and injured eight other children and two adults at a dance class in Southport.

The police on Monday arrested a 17-year-old who was born in Cardiff, Wales, on suspicion of murder and attempted murder. In line with British law regarding minors, the police did not identify the suspect, and subsequently they warned that a name being circulated on social media was incorrect.

Alex Goss, the assistant chief constable of the Merseyside police, said on Tuesday night, “There has been much speculation and hypothesis around the status of a 17-year-old male who is currently in police custody and some individuals are using this to bring violence and disorder to our streets.”

He added, “We have already said that the person arrested was born in the U.K. and speculation helps nobody at this time.”

Many of those involved in the unrest, he noted, “do not live in the Merseyside area or care about the people of Merseyside.”

The outbreak of violence, in which rioters set police cars on fire, destroyed vehicles belonging to locals, threw bricks at the mosque and damaged a convenience store, was deeply distressing for a community still grappling with the raw emotions after Monday’s attack.

The police have said that they are still investigating the motive for the attack, but said it was “not being treated as terrorist-related.”

In a statement on Tuesday night, the British prime minister, Keir Starmer, condemned the rioting and vowed to hold those who took part accountable.

“Those who have hijacked the vigil for the victims with violence and thuggery have insulted the community as it grieves,” Mr. Starmer wrote in a statement. “They will feel the full force of the law.”

The North West Ambulance Service, which covers the region, said that 39 patients, all of whom were police officers, had been treated for injuries. Twenty-seven of those officers had to be taken to the hospital.

The violence began shortly after thousands had gathered in the town for a vigil to honor the victims of the attack, with many crowding a central square grasping bouquets of flowers and teddy bears.

A flood of disinformation online about the perpetrator of the attack was amplified by far-right influencers, including Tommy Robinson, an anti-Islam agitator and founder of the English Defence League, and Andrew Tate, another extremist online personality.

Merseyside Police later said that 22 of its officers had been injured and that eight had sustained serious injuries including fractures, lacerations, a suspected broken nose and a concussion.

Others had head injuries, facial injuries and one was knocked unconscious, the force said.

The violence occurred a short walk from where the initial stabbings took place on Monday. As the evening light turned to darkness on Tuesday, smoke from the riot drifted over the makeshift memorial that had sprung up, the acrid black fumes visible on the horizon over the piles of flowers.

Mr. Goss of the Merseyside Police said that a number of off-duty police officers had been called in to support their colleagues, and he applauded their dedication while criticizing those who took part in the disorder.

“This is no way to treat a community,” he said, “least of all a community that is still reeling from the events of Monday.”