They arrived at polling stations long before dawn, slept in the streets so they could be the first in line, and then cried as they cast their votes.

On Sunday, millions of Venezuelans headed to the ballot box in an election that will determine the fate of the socialist movement that has governed oil-rich, crisis-laden Venezuela for 25 years.

Polls started closing at 6 p.m., though some stayed open to accommodate people waiting to cast a ballot.

For the first time in more than a decade, the country’s authoritarian president, Nicolás Maduro, faces a strong challenger, Edmundo González, a previously little-known former diplomat who has the backing of a popular leader, María Corina Machado.

The vote represents an existential moment for Chavismo, the socialist movement that swept to power in Venezuela in 1999. Founded by former President Hugo Chávez, Mr. Maduro’s mentor, the movement promised to lift millions out of poverty.

For a time, it did. But, over the course of a generation, the movement shattered the nation’s democracy, presided over an economic contraction unlike any seen outside of war and became the source of one of the largest migrant crises in the world.

The country’s travails have drawn voters to Ms. Machado, a conservative former lawmaker who has promised to restore democracy and bring millions of Venezuelans back home. When the government barred her from running, her coalition managed to get Mr. González on the ballot instead.

On Sunday, turnout appeared to be high.

“There could be an earthquake, a landslide, rain — we are going to vote,” said Henry Mayora, 74, who arrived at his polling station in Caracas, the capital, at 2:30 a.m., hours before polls opened at 6.

Mr. Mayora, who walks with a cane and said he supports the opposition, was first in his line to cast a ballot.

For years the government of Mr. Maduro has used coercion, suppression and confusion to win elections. And throughout the day on Sunday, there were many complaints of problems with the vote, including polling places that opened hours late and voting machines that did not work.

Phil Gunson, a longtime analyst in Venezuela for International Crisis Group, said the irregularities were “within the ‘normal’ range” for an election in Venezuela in recent years.

Mr. Maduro has rarely, if ever, mentioned an outcome in which his party loses. In one recent campaign speech, he threatened that there would be a “blood bath” if his party lost.

But on Sunday, speaking to reporters, he appeared to strike a more conciliatory tone.

“I recognize and will recognize the electoral arbiter,” he said, a reference to the country’s election body, “and I will make the electoral arbiter’s holy word be respected.”

The electoral council is headed by an acolyte of Mr. Maduro’s party, Elvis Amoroso.

At the Liceo Andrés Bello, a voting center in Caracas, a journalist with The New York Times watched roughly 15 men in unmarked black jackets temporarily block access to the center in the early morning. One volunteer vote monitor was punched.

Finally the crowd erupted in a chant — “We want to vote!” — and a long line of people began moving inside, more than an hour and a half after the official start of the balloting.

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

In one voting place in the city of Carúpano, in the north, 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 monitor lacking credentials from the country’s electoral body.

In the nearby city of Cumaná, five people said that 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 blocked by supporters of the government.

At another polling place in Cumaná, roughly 50 armed police officers and national guardsmen had formed a long line outside by midmorning, wearing helmets and bullet-resistant vests, clearly projecting the state’s strength to anyone considering voting against those in power.

In the city of Maracaibo, in the west, voters reported having their voting places moved without their knowledge. 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.”

In other places, voting went more smoothly. At one of Caracas’s largest voting centers, in the working-class Petare neighborhood, Rony Velázquez, a personal trainer, said he chose to vote for the government.

He said that he was sympathetic to the opposition but sought improvements within the current political system, out of fear that a different government would plunge the country into a new period of uncertainty.

“It would take them years to change things,” he said.

In an interview a day before the vote, Nicolás Maduro Guerra, a legislator and the son of the president, said he was sure his father would win re-election.

“We are confident in the victory, not because we are triumphalists, but because we have done our homework,” he said. But, in the case of a loss, “we will recognize the result and become the opposition,” he said. “Life goes on.”

If the main opposition candidate, Mr. González, wins and is allowed to take office, he is likely to face immense challenges, including the fact that nearly all institutions — including the legislature — remain loyal to Mr. Maduro.

Mr. Chávez, the founder of the country’s socialist project, swept to power in 1999 following a democratic election, vowing to remake a system led by a corrupt elite. Today, his movement runs a state widely viewed as corrupt, his party’s leaders are the elite — and Ms. Machado is promising to oust them.

Mr. Maduro has maintained his grip by punishing dissidents, crushing protests and co-opting state institutions. At the same time, the socialist model he once hailed has given way to brutal capitalism, economists say, with a small state-connected minority controlling much of the nation’s wealth.

Mr. Maduro is holding an election in part because of international pressure: The United States has promised to lift punishing economic sanctions on the country’s oil industry only if a competitive presidential vote is held.

Many analysts say Mr. Maduro never thought Ms. Machado and Mr. González would gain so much momentum.

And many in Venezuela believe that Mr. Maduro has little incentive to allow for a result that shows he has lost. The United States has accused him of narco-trafficking and has offered $15 million for information leading to his arrest. The International Criminal Court is investigating him for crimes against humanity. Both make him vulnerable to prosecution if he leaves office.

Francisco Rodríguez, a Venezuelan economist and professor of international affairs at the University of Denver, said he could foresee three possible outcomes.

First, the vote could represent the beginning of a democratic transition. Second, it could completely consolidate Mr. Maduro’s power.

Or, he said, “this could be — and is what I fear most — the moment of an escalation and a deepening of the conflict, the destructive conflict that continues to do more damage to society and the Venezuelan economy.”

Whatever result is announced, it is very likely to be disputed by the other side, possibly leading to protest and a violent response from the armed forces.

The next president wouldn’t assume power until January, leaving a lengthy period of uncertainty.

In recent interviews across the country, some supporters of Ms. Machado vowed to take to the streets if Mr. Maduro declared victory.

Luis Bravo, who attended a recent Machado campaign event, said that if Mr. Maduro claimed a win and protests began, he would join them.

“I am praying that it doesn’t come to that because, obviously, a lot of people are going to die. But if I have to, I have to.”

Reporting was contributed by Isayen Herrera and Alejandro Cegarra from Caracas, Venezuela, Nayrobis Rodríguez from Sucre, Venezuela, Sheyla Urdaneta from Maracaibo, Venezuela, and Genevieve Glatsky from Bogotá, Colombia.

The surveillance drone appeared high above the Ukrainian air base without warning in early July. Minutes after it relayed targeting data back to a Russian base, a barrage of ballistic missiles struck the airfield, Ukrainian officials said, recounting the episode.

“That first hit was so powerful that even our windows were trembling,” said Valeria Minenko, 21, who lives near the air base in Myrhorod, central Ukraine, one of many targeted in relentless attacks by Russia in recent months.

“Now they’re hitting the air base with the rockets all the time,” Ms. Minenko said.

Russia has been saturating the skies over Ukraine with surveillance drones, exploiting gaps in air-defense systems, to launch increasingly sophisticated attacks on Ukrainian positions. Its dominance in the air along parts of the front has allowed it to bombard Ukrainian positions with hundreds of powerful guided bombs every day, helping its ground forces to make slow and costly gains.

Ukraine’s strategy was to counter Russia in the air war with the aid of long-coveted F-16 fighter jets from the West that it says it will deploy this summer.

But the assaults on Ukrainian air bases underscore Russia’s determination to limit the impact of the planes even before they enter the fight. They also highlight the challenges Ukraine faces as it prepares to deploy the sophisticated aircraft for the first time.

Ukraine is hoping the F-16s, which come with powerful electronic warfare systems and an array of other weapons, can be used in coordination with other Western weapons like Patriot air-defense systems to expand the area deemed too dangerous for Russian pilots to fly. They also hope the jets will add another layer of protection for Ukrainian cities and critical infrastructure from relentless missile and drone attacks.

But a shortage of trained pilots and a limited number of jets will constrain the immediate impact, experts say.

“Russia has had so much time to fortify its defenses, especially along the frontline areas,” said Hunter Stoll, a defense analyst at RAND, a research organization. “The F-16s and their pilots will face stiff resistance from Russian air defenses, both on the ground and in the sky.”

Ukraine says it is “in the process” of moving the first F-16s into the country, about two and a half years after it first pleaded for the aircraft. It has been a year since the Biden administration finally reversed policy and allowed Western allies to transfer American fighter jets to Ukraine.

“Today, we can already say clearly, we have entered the club of countries that have F-16s,” Yuri Ihnat, a representative for the Ukrainian Air Force, said in an interview. “This is a turning point for our nation.”

The arrival of the planes — the exact number has not been publicly revealed — comes at a moment of deep uncertainty in the war. Russian forces are engaged in furious assaults all along the 600-mile front, the Ukrainian energy grid is crippled by years of unrelenting bombardment and a presidential election in the United States could reshape future military assistance.

In addition to the Russian attacks on the Ukrainian airfields, Ukraine will also be constrained by the small number of trained pilots, according to Ukrainian and U.S. military officials. About 20 airmen in the various U.S., Dutch and Danish training pipelines are expected to be ready this year, according to U.S. officials.

Air commanders say they typically allot at least two pilots per aircraft — for crew rest, training and other matters. So that would allow Ukraine to fly only about 10 F-16s, at most, on combat missions this year.

Another major limiting factor, these officials say, is the number of trained maintenance and support personnel on the ground to keep the F-16s flying.

“It’s not just the pilots you have to have,” Gen. Charles Q. Brown Jr., the chairman of the Joint Chiefs of Staff and a longtime F-16 pilot, said last month. “Maintenance is also a key part of that, and training the maintainers.”

Gen. Serhii Holubtsov, chief of aviation of Ukraine’s air force, said Ukrainians “do not wear rose-colored glasses” and understand that the F-16 is “not a panacea.”

The strategy, he told Donbas Realiy, a branch of Radio Liberty, can be thought of in three phases — “crawl, walk, run” — and it will take time.

“We haven’t learned to crawl yet,” he said.

Before the jets can start to play a role in shaping the battlefield, Ukraine needs to be sure they can be protected. While Russia has been attacking Ukrainian airfields since the first hours of the war, the early July attack on Myrhorod was different, Ukrainian officials said.

“The enemy came up with a new tactic,” Mr. Ihnat said.

Specifically, he said, the Russians are improving missiles and reconnaissance drones, “making it so that we cannot influence them with electronic warfare.”

They are also preprogramming surveillance drones to fly deep into Ukraine without emitting telltale electronic signatures, making them harder to detect.

Gen. Oleksandr Syrsky, Ukraine’s top military commander, said this past week that Ukraine urgently needed to find new methods of destroying enemy drones.

Mr. Ihnat said that the Ukrainian air force had effectively adopted deception tactics — like building model planes to act as decoys, camouflaging aircraft and moving them — to protect its depleted fleet of Soviet-era aircraft, and would do the same for the F-16s.

“If someone wants to laugh at this, let them,” he said. “Thanks to the models, the enemy has already lost dozens or even hundreds of their missiles.”

Ukraine is also employing 1970s-vintage Yakovlev Yak-52 training planes to hunt Russian surveillance drones, he said.

The propeller-driven aircraft have been hunting Russian surveillance drones across southern Ukraine, with both Ukrainian and Russian forces posting videos of the aerial clashes.

General Holubtsov said he expected attacks on the airfields to increase. For that reason, he said, Ukraine will not keep all the promised F-16s in the country.

“There are a certain number of aircraft that will be stored at secure air bases, outside of Ukraine, so that they are not targeted here,” he said. “And this will be our reserve in case of need for replacement of faulty planes during routine maintenance.”

President Vladimir V. Putin of Russia has said that the storage abroad of planes or other Ukrainian military assets could “pose a serious danger of NATO being drawn further into the conflict.”

The Biden administration’s approach to arming Ukraine has been driven in large part by concerns about potential escalation with Moscow, which is why it resisted allowing the transfer of F-16s from allies for so long.

Retired Lt. Gen. David A. Deptula, the dean of the Mitchell Institute for Aerospace Studies in Washington, said the delay “has given Russia the gift of time.”

“We gave them time to dig in and establish defenses that are now much more difficult to unravel,” he said.

American, Dutch and Danish officials have been working with Ukrainian counterparts to hammer out the details of synchronizing the arrival of the promised aircraft, equipping them with air-to-air and air-to-ground munitions, and thinking through the most efficient and effective use of the initial group of planes, the U.S. and Ukrainian officials said.

After spending some time getting used to the aircraft, General Holubtsov said, the F-16s can be used in the effort to push back the Russian attack planes that have been bombing Ukraine.

General Holubtsov said that F-16s alone would not be enough to drive back the Russian warplanes. They will work in concert with ground-based air defenses like the Patriots, coordinating efforts with a powerful Western information exchange network called Link 16.

The process will take time, he said, and there are a host of factors that could complicate the effort, including Ukraine’s shortage of air-defense systems, which it needs desperately to protect civilian as well as military assets.

But if the Russian planes can be driven further back from the front, the general said, “it can be considered a turning point and a victory — if not superiority, then parity in the air space.”

Dzvinka Pinchuk contributed reporting. Nataliia Novosolova contributed research.

Senior officials from Israel, Egypt, Qatar and the United States met in Rome on Sunday to continue negotiations over a cease-fire in Gaza, according to three officials involved in or briefed on the talks and a statement from the Israeli government. The talks came as tensions mounted in the region amid growing violence along the border between Israel and Lebanon.

The officials at the daylong talks in Rome were pushing to forge a truce in which Israeli hostages held captive by Hamas would be exchanged for hundreds of Palestinians jailed by Israel under a plan that has been discussed for months. Qatar hosts part of the Hamas leadership and, along with Egypt, plays a key role in mediating between the two sides.

The Israeli government announced on Sunday evening that its representative at the meeting, David Barnea, Israel’s foreign intelligence chief, had already returned home and that negotiations would resume in the coming days. The statement did not give further details.

Despite progress in recent weeks, the monthslong negotiations remain stalled over several critical issues, particularly the extent to which Israeli forces would remain in Gaza during a truce, according to seven officials involved in or briefed on the talks.

Earlier in July, Israel hardened its position on maintaining checkpoints along a strategic highway south of Gaza City, weeks after suggesting that it could compromise. It was unclear on Sunday if Mr. Netanyahu had allowed negotiators to show greater flexibility on the matter during the talks. Mr. Netanyahu faces pressure from members of his right-wing government to stick to a tougher line.

The length of the truce is also a source of dispute: Hamas wants a permanent truce, while Israel wants the option to resume fighting.

Israel has also refused to guarantee that its troops will leave the Gaza-Egypt border during a cease-fire, fearing that Hamas would smuggle arms across the frontier in the absence of Israeli forces.

Israeli negotiators have privately discussed leaving the border zone if they can first install electronic sensors to detect future efforts to dig tunnels, as well as construct underground barriers to block tunnel construction, according to three officials briefed on the talks. But no agreement has been reached, the officials said.

Israel wants to maintain military checkpoints along a strategic highway inside Gaza in order to prevent Hamas fighters from ferrying weapons toward Gaza City, according to four Israeli officials and an official from one of the mediating countries. After appearing more flexible on the issue earlier in the summer, Israel’s stance hardened again roughly three weeks ago, while Hamas never agreed to compromise, the officials said.

All the officials spoke on condition of anonymity in order to speak more freely about sensitive matters.

The meeting in Rome came as Western diplomats scrambled on Sunday to prevent a surge of fighting along the Israel-Lebanon border, officials said, after a rocket from Lebanon on Saturday killed at least 12 people in an Israeli-controlled town, most of them children. Israel retaliated early Sunday with strikes across Lebanon.

Before the latest strikes, mediators between the two sides had been hoping that a truce in Gaza could provide the impetus for an easing of tensions along the Israel-Lebanon border, even as the risk of escalation there remains higher than ever.

Six Israeli officials said that Prime Minister Benjamin Netanyahu was the main reason for Israel’s hardened stance at the Rome talks, and that top security officials are pushing for the prime minister to show greater flexibility in order to secure a deal. Mr. Netanyahu’s room for maneuver is limited by the members of his right-wing coalition government; some of them oppose a truce that would allow Hamas to survive the war intact and have threatened to bring down the government if their wishes are not met.

Mr. Netanyahu’s office did not respond to requests for comment. But on Thursday, he promised families of hostages held in Gaza that his government would not introduce new conditions or obstacles to achieving a framework agreement for a cease-fire, according to Jonathan Dekel-Chen, whose son Sagui was abducted during the Hamas-led Oct. 7 attack.

Mr. Netanyahu’s pledge, Mr. Dekel-Chen said, was made in the presence of President Biden, his national security adviser, Jake Sullivan, and six families with relatives held in Gaza.

“He committed in front of the president to act with more urgency than he has in the past,” Mr. Dekel-Chen said in a phone interview on Saturday.

The talks in Rome came as tens of thousands of people have been forced under Israeli orders to evacuate several neighborhoods in southern and central Gaza, according to the United Nations.

An Israeli order on Saturday was the latest in a series of such directives recently that have forced displaced Palestinians to again relocate.

The order includes an area around the city of Khan Younis that Israel had previously designated a “humanitarian zone” for Palestinian civilians, who have faced nearly a year of unrelenting war and struggled to avoid disease and find food and clean water.

Tens of thousands of people have been heading on foot toward Al Mawasi, an already overcrowded stretch of tents near the sea in Gaza that has served as a makeshift refuge of last resort for months. About 182,000 people were displaced from the southern city of Khan Younis to Al Mawasi in just a few days last week, the United Nations estimates.

But the United Nations also said hundreds remained stranded in areas that had been ordered evacuated, including about 300 sheltering at various schools.

Some were forced to stay because of disabled relatives. Kamel Abu Jamea, 73, a Khan Younis resident, said his wife, Amna, 73, was too sick to walk, leaving them unable to evacuate despite the shelling and gunfire he could hear outside. He had tried to find a ride for them to a safer area, but had no luck. And their food, water and medication were all running out.

“My wife can’t even walk five meters,” he said. “I can’t leave her and go.”

The Israeli evacuation orders have further complicated the work of aid groups trying to serve the Khan Younis area.

Twelve distribution points that had been set up to give out food have suspended their operations, along with eight hot meal kitchens and nutrition programs for children and pregnant women at two shelters, the United Nations said. Ten water and sanitation facilities, and at least 17 shelters have also stopped working, it said.

Vivian Yee contributed reporting from Cairo, and Iyad Abuheweila from Istanbul.

The Olympic Games have long been governed by a tacit code: If fans can’t say anything nice, they shouldn’t say anything at all. Jeering, whistling and catcalling at athletes who have spent years to make it to the pinnacle of their sports is “unacceptable,” as Thomas Bach, the president of the International Olympic Committee, once put it. To boo is, well, taboo.

As far as the French are concerned, though, there appears to be one exception: anyone wearing the sky blue and white of Argentina.

In the opening few days of the Paris Games, Argentina was booed before, during and after a men’s soccer game in Marseille. It was heartily booed for three days straight every time its men’s rugby sevens team appeared at a packed Stade de France. And it was booed again whenever one of those rugby players had the temerity to touch the ball.

Its anthem was booed once more — although a little more gently — when Argentina’s team made its debut in the men’s volleyball tournament at the South Paris Arena on Saturday evening.

The hostility has left some of the country’s opponents wondering what is going on. Nick Malouf, an Australian rugby sevens player, said he “did not know the background” behind the tension. Antony Mboya, representing Kenya in the same sport, assumed the local French crowd was just “backing an underdog.”

In reality, the animosity is much more targeted. Both sides have come to understand that France, at this moment in time, does not much like Argentina. “It has become a real rivalry for us,” said Jules Briand, a French fan who traveled both to watch his team compete in rugby sevens and to indulge in a little jeering.

Where fans differ is on the root causes for what is, in a sporting sense, something of a new phenomenon.

France and Argentina do not share any real historical antipathy in soccer or rugby, the two most tribal sports they have in common. Both, traditionally, reserve their enmity for others: Argentina for Brazil (and England), France for Germany (and England).

Argentina’s version of events is relatively simple: France is bitter over its defeat at the hands of Argentina in the final of the 2022 World Cup.

Marcos Moneta, a member of Argentina’s rugby sevens team, put it bluntly: “Maybe they are hurt by Lionel Messi.” His coach, Santiago Gómez Cora, was a little more diplomatic. “It is a part of soccer folklore that has passed over into rugby,” he said.

There is some evidence for that assessment. Emiliano Martínez, one of the stars of that Argentine victory in Qatar in 2022, was jeered while playing in France in May, though the French trace that less to the fact of the defeat than to what was deemed an intolerable level of gloating by Argentina’s players in its aftermath. “The players were not very gracious,” Briand said.

France’s explanation is a little more complex. “There are a few reasons,” said Gauthier du Pradel, a French fan who was idling outside the Stade de France during a break in the rugby tournament last week. He admitted, a little sheepishly, that he had joined the chorus of derision when he saw the Argentine players emerge.

He pointed to a couple of rugby-specific skirmishes — lingering resentment over competition in various disciplines of the sport and the arrest of two French players in Argentina on accusations of sexual assault — but he also mentioned a more recent, high-profile trigger.

A few weeks ago, after Argentina had won soccer’s Copa América in the United States, the team’s players were captured on a livestream singing a derogatory song about France’s players. It included lyrics that were racist and transphobic. “That song caused a lot of noise on social media,” du Pradel said.

That may be an understatement. Enzo Fernández, the player who filmed the incident, publicly apologized, but only after French officials criticized him. France’s soccer authorities have filed a legal complaint over “unacceptable racist and discriminatory remarks.”

Argentina has proved even more unwilling to take responsibility. The country’s conservative vice president, Victoria Villarruel, insisted that France was in no position to censure Argentina over race given its “colonialist” history.

Javier Milei, the libertarian Argentine president, removed a lawmaker who had called on Messi himself to apologize. “No government can tell the Argentine national team, world champion and two-time champion of Copa América what to comment, what to think or what to do,” Milei’s office said at the time.

Milei has since tried to distance himself from the controversy: he was scheduled to meet with Emmanuel Macron, his French counterpart, while visiting Paris for the opening ceremony. Argentina’s athletes, maybe with the exception of Moneta, have done what they can to downplay it, too.

“I’m happy if they cheer for us or if they insult us,” said Luciano De Cecco, the captain of Argentina’s men’s volleyball team. “I don’t get mad, and nor do I enjoy it. It’s part of the game.” Gómez Cora, the rugby coach, insisted the boos were preferable to silence. “I’d rather have people for you and against you than a crowd sitting there bored,” he said.

There is, even the French fans admit, a slight element of pantomime to it. “It’s not a real hatred,” said du Pradel, the French fan. “If I saw an Argentine now, I’d have a beer with them.” The anger over the song, though, is not an act. For that, he said, “they are going to get booed everywhere.”

Less than three years ago, Wassif Frahat spent $3 million to open a lavish, two-story restaurant, the Ali Baba. With an impressive, pillared entryway, polished stone floors, glittering chandeliers and colorful frescoes on the high ceilings, the restaurant was his commitment to a better future.

The Ali Baba, in Jenin, is just a few minutes’ drive from the Jalameh checkpoint, which in normal times allows Israeli Arab citizens entry to the West Bank. The atmosphere is Palestinian, and the shops, restaurants and services are significantly cheaper than in Israel. The crossing also allows Palestinians with valid entry permits to go to jobs in Israel.

But after Hamas invaded Israel from Gaza on Oct. 7, the checkpoint was closed. Israel withheld most tax revenue from the authorities in the West Bank, in an effort to weaken them and clamp down more broadly on Palestinians. The economy in the territory’s north collapsed, and the better future that Mr. Frahat expected now seems further away than ever.

The war that followed the invasion is devastating Gaza, but it is also impoverishing the West Bank, which has become a kind of second front in Israel’s battle against Palestinian militancy.

The Palestinian Authority, which administers parts of the West Bank but does not run Gaza, has been paying only about 50 percent of the salaries it owes its estimated 140,000 employees. In the West Bank as a whole, which has a population of about three million, 144,000 jobs have disappeared since October, and 148,000 Palestinians who were working in Israel have lost their jobs, according to the World Bank. Before Oct. 7, unemployment in the West Bank was about 13 percent, compared to 45 percent in Gaza.

Mr. Frahat, 51, once had 53 employees at his restaurant and an older one in the city center. “Now I only have 18 because business is down by 90 percent,” he said.

Israeli Arabs are not his only lost customers; local Palestinians have stopped coming, too. They lack money, he said, and fear continued incursions by Israel’s military. Its forces are trying to tamp down increasing militancy among young armed Palestinians who largely run the sprawling refugee camps in Jenin and the cities of Tulkarm and Nablus.

The Israeli Army killed seven people in a raid in Jenin on July 5, after a larger operation in late May that killed 12.

“People are afraid to leave their homes,” Mr. Frahat said.

In large parts of Jenin, and especially near its refugee camp, Israeli troops using tanks and armored bulldozers have ripped up roads, cut water and sewage pipes, broken power lines and smashed many storefronts and United Nations offices, including a recently renovated medical clinic. The scene is similar in Tulkarm, with its two refugee camps.

Shlomo Brom, a retired Israeli brigadier general and senior researcher at the Institute for National Security Studies, said that the army was engaged in “preventive actions” to head off a new wave of suicide bombings carried out by “armed groups producing explosives.”

Jenin and some of the camps are bastions of armed resistance to the occupation. Israel has conducted frequent raids over the years, but they have become more common since Oct. 7. Israeli officials say the raids are part of counterterrorism operations against Hamas and an extension of the war. Hundreds of Palestinians have been detained.

The raids have piled only more misery on a failing economy. Amar Abu Beker, 49, the chairman of the Jenin Chamber of Commerce, which represents 5,000 businesses, said that 70 percent of them were struggling to stay afloat.

The chamber is working to repair the key roads that Israeli forces have wrecked because the Palestinian Authority has little money for such work, Mr. Abu Beker said. In addition to the damage done by the checkpoint closure, the economy had been constricted by monthslong general strikes in 2022 and 2023 in sympathy with Palestinians killed in Israeli raids.

“The Palestinian Authority is holding on by its fingernails,” Mr. Abu Beker said. “Without money, you can’t operate.”

In a recent report, the World Bank said that the authority’s financial health “has dramatically worsened in the last three months, significantly raising the risk of a fiscal collapse.” It cited the “drastic reduction” in tax transfers from Israel and “a massive drop in economic activity.”

The measures to starve the Palestinian Authority of funds, pushed by far-right members of the Israeli government who want to annex the West Bank and resettle Gaza, have alarmed the Biden administration. U.S. officials want the authority to play a role in running postwar Gaza and worry that an economic crash in the West Bank could lead to more violence.

U.S. officials have pressured the Israeli government to release withheld taxes, which make up about 70 percent of the authority’s income. On July 3, Israel agreed to release $116 million, but the Palestinian Authority said it was owed nearly $1.6 billion.

Anas Jaber, 27, is among the Palestinians who have lost their jobs in Israel. He had been making up to 7,000 shekels a month, or about $1,870, as a housekeeper at a Tel Aviv hotel.

“Now I sit at home and live off savings,” he said. “I’m not married, thank God.” His job has been filled by Filipinos and Indians, and he has applied to move to Canada. “Inshallah,” he said. “I’m sick of checkpoints, and I want to sleep at night.”

There has been no water for a week, he said. Near his mother’s house, where he is staying, is graffiti in Hebrew and Arabic on a bullet-pocked wall that says, “Alleyways of death.”

Um Ibrahim, 60, said she used to get 750 shekels every three months from the Palestinian Authority for medicine to treat her diabetes and high blood pressure.

“For the past nine months, nothing,” she said. “The authority is having an economic crisis, so I’m scared I won’t get any help.” And if it collapses? She laughed bitterly. “OK, then, bye-bye.”

The governor of Jenin, Kamal Abu al-Rub, 58, admitted that with checkpoints closed, first during the Covid pandemic and now after Oct. 7, the city is struggling.

“The veins that let us live are Palestinians from Israel, our lifeblood,” he said, sitting in his large office as an American armored personnel carrier guarded the entrance. The city’s Arab American University is mostly shut now, with only a third of its regular 6,000 students, who in normal times pay rent and shop in stores.

Israel did allow the Jalameh checkpoint to open in late May, but only on Friday mornings, when the shops are closed and most people are at mosques, and on Saturdays from 9 a.m. to 5 p.m.

A large photograph of Mr. Abu al-Rub’s son Shamekh hangs in his office. A doctor who trained in Jordan, Shamekh, then 25, was shot and killed by Israeli troops in November, in nearby Qabatiya, when trying to reach his brother, Muhammad, who had been shot in the leg, Mr. Abu al-Rub said. “They shot my two sons in front of my house,” he said.

He praises the Palestinian security forces, two of whose commanders were in the room monitoring the interview, for keeping law and order on badly reduced salaries. But he acknowledges that the security forces do not maintain a presence in the refugee camps, where Israel says the militants have established control, and he blames Israel for all the trouble.

Asked why young fighters from the camp, known as shabab, sometimes fire on his headquarters, Mr. Abu al-Rub said, “It is Israel that is giving the shabab weapons to fire at the P.A.”

Israeli officials deny such charges but would not comment on individual raids or deaths.

At the entrance to the camp, in the hot sun, Mahmoud Jalmaneh, 56, described how his life had changed as he tried to sell cheap tobacco from a dusty glass cabinet on wheels — 20 cigarettes for 4 shekels, about a dollar, compared to more than $8 for Marlboros, which he does not sell.

Born and raised here, he has seven children, and last July, Israeli troops were caught in a firefight in front of his house and blew it up, he said. “I was a homeowner and now I’m renting, and I have no more money to pay when the landlord comes,” he said.

“The checkpoints are closed; we can’t work in Israel or leave the country,” Mr. Jalmaneh said. “There’s no money, no salaries.”

“We are lonely. We are a people isolated and under occupation. We are fighting the whole world.”

Rami Nazzal contributed reporting from Tulkarm and Jenin, and Natan Odenheimer from Jerusalem.

The top diplomatic and defense officials from the United States and Japan announced on Sunday that their nations would take concrete steps to bolster their military alliance because of the growing threat from China in the region.

Those steps include establishing a joint force headquarters that would answer to the American commander in the Indo-Pacific, according to a statement issued by the two governments’ top officials and the committee that they oversaw. They also call for increasing co-production of air-to-air missiles and air defense interceptor missiles.

“The U.S. will have a direct leadership role in planning and leading U.S. forces in both peacetime and in potential crises,” Lloyd J. Austin III, the U.S. defense secretary, said of the new headquarters at a news conference later Sunday. “And that will give us an opportunity to work more closely together to ensure greater peace and stability.”

The statement framed these changes in the alliance relationship mainly as a response to aggressive moves by China in East Asia. The statement focused on China’s actions in the East China Sea, South China Sea and beyond while also mentioning hostile activity by Russia and North Korea.

The governments reaffirmed the importance of the mutual-defense clause in their treaty because of the “increasingly severe security environment caused by recent moves of regional actors,” they said.

One of the top issues cited was the East China Sea, which Japan and China both claim part of. The American and Japanese senior officials said their governments reiterated their strong opposition to China’s “intensifying attempts to unilaterally change the status quo by force or coercion.”

Mr. Austin and Antony J. Blinken, the U.S. secretary of state, were in Tokyo on Sunday to meet with their Japanese counterparts in what is commonly called a 2+2 dialogue.

Such meetings take place regularly, but this one had added significance because of President Biden’s announcement last Sunday that he would not seek re-election. That means America will have a new leader in January, most likely either Kamala Harris, the current vice president, or Donald J. Trump, Mr. Biden’s predecessor. So foreign leaders have many questions about how a new president will approach foreign policy and America’s alliances.

Allied officials know little about Ms. Harris, though they assume she would mostly continue Mr. Biden’s policies, since she is part of his administration. In Asia and Europe, the focus of those policies has been to enhance alliances. The officials are more concerned about the potential return to power of Mr. Trump, who has often criticized his nation’s military alliances as costly and not to America’s benefit.

Japan and South Korea, two countries where the United States has troops stationed, are among the most worried. Wary of a potential war involving China, North Korea or both, many Japanese and Korean officials see the presence of U.S. troops and weapon systems as a crucial deterrent.

Mr. Biden’s actions have shown awareness of this. During a state visit to the United States by the Japanese prime minister, Fumio Kishida, in April, the two leaders announced upgrades to military cooperation. In January, Japan signed an agreement with the United States to buy 400 Tomahawk cruise missiles at a cost of $1.7 billion.

The statement from Mr. Blinken and Mr. Austin and their Japanese counterparts, Yoko Kamikawa and Minoru Kihara, laid out details of further cooperation on weapons. One notable line said Japan planned to help produce more Patriot interceptor missiles, which the United States and allied nations have been supplying to Ukraine to aid in warding off Russian air attacks.

Mr. Blinken and Mr. Austin plan to fly next to the Philippines, where they are to hold another 2+2 dialogue. Chinese coast guard vessels and Philippine naval ships have clashed recently, but without gunfire, in contested waters of the South China Sea. The United States has issued statements reminding China that its treaty with the Philippines has a mutual-defense clause.

Follow live updates of the women’s gymnastics qualifying at the 2024 Paris Olympics.

With a toe-tapping Beyoncé song blasting in the arena, Simone Biles leaped up to the balance beam and wobbled, leaning over and circling her arms like windmills as if she were trying not to fall off a cliff.