In Riomaggiore, one of the five vertigo-inducing villages that make up Cinque Terre, which hug the steep cliffs of Italy’s northwestern coast, just about everyone has a memory of the Via dell’Amore, or Love’s Lane.

With breathtaking sunset views, the seacoast trail to neighboring Manarola was popular with local couples. “Otherwise what kind of love lane would it be?” said Marinella Cigliano, a 60-something who remembers getting caught by her mother while making out with a long-ago boyfriend.

As young mothers, “we brought our children in strollers, a place for afternoon walks,” said Roberta Pecunia, whose grandfather Brizio was among the local villagers who in the 1930s carved the path out of the rock face to link the towns. And when Vittoria Capellini’s father was a young boy, walking the trail to school, his mother would tell him to “run like crazy” over the sections of the trail where the cliff face was particularly unstable.

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In a forest in western Ukraine, a few dozen young men and women stood at attention in two lines in the fading evening light. Some had fake guns slung over their shoulders.

Among them was Olesya Vdovych, who had spent the day with other members of the scouting organization Plast, hauling logs, running drills and learning about first aid as part of a two-week camp last August.

“I’m eager to be prepared,” Ms. Vdovych said at the time, her long blond hair tied in two braids under a forest green cap. With a number of her friends and family fighting in the war against Russia, she said she felt it was important to be ready for any situation.

For young Ukrainians like Ms. Vdovych, the once-carefree summers of childhood and young adulthood were forever altered by Russia’s invasion of the country more than two years ago. Since then, the war has ground on with little change in Ukraine’s fortunes, even as Ukrainian forces made a rare incursion into Russia last week, taking some territory, and engaging in furious fighting with Russian forces. Ukraine has struggled to hold back Russian forces in the east, and devastating airstrikes continue to bombard cities far from the front lines. In April, Ukraine lowered the draft age for young men, to 25 from 27.

Against this backdrop, scouting camps like the one run by Plast have taken on a new resonance. Traditions like hiking and campfires, intended to foster an appreciation for nature, have been supplemented by activities with a more patriotic tone. New camps have also sprung up, some intended to prepare youngsters for battle, with a focus on team-building, first-aid skills and military preparedness.

Some camps are run by the youth branches of right-wing groups with a distinctly nationalistic bent as they take on the mission of molding future Ukrainian soldiers. And some have intensive — sometimes punishing — physical challenges.

This year, Ms. Vdovych will return to the Plast camp in the forest, this time as an instructor leading scouts ages 15 to 21 through the same exercises she did last year.

“There is no question of if I will go to war,” said Ms. Vdovych, 20, reflecting recently on the camp. “It’s not if, but when.”

“Everyone has to be involved and ready,” she added.

Plast, founded in 1911 in western Ukraine, has roots in the global scouting movement started by Robert Baden-Powell, a British lieutenant general.

The group was officially banned for decades as Polish, German and Soviet forces controlled the area, said Olga Svinzinska, a historian and Plast member who is an authority on the group’s history. Still, it thrived within the Ukrainian diaspora and among those who pushed for an independent state. Plast was revived when the Soviet Union collapsed and the Ukrainian state was founded in 1991.

Interest in the group grew with a surge in patriotism after the 2014 Maidan uprising, which toppled a pro-Russian leader and led to the Russian-backed separatist conflict in eastern Ukraine. Dozens of former Plast scouts have volunteered in the struggle, according to the organization, and at least 58 have been killed since the fighting began.

Ksenia Dremliuzhenko, a chairman of the regional Plast council, said she had seen a noticeable shift in the mood of scouting camp participants in the past year, reflecting the challenges of the war with Russia.

“Everyone feels this fatigue, but there is an understanding of what we are fighting for,” she said. “We cannot give up when our friends have already died for our freedom.”

Many of the camps are rich with symbolism and infused with folk tradition.

At a Plast camp aimed for scouts ages 15 to 20, in the Lviv region, participants wear vyshyvankas — the intricately embroidered shirts of the country’s national dress — as they recreate Kupala Day, a Ukrainian folklore crowning ceremony.

These days, the camps have also taken on an additional role as war upends Ukraine’s educational system. Thousands of schools across the country have been damaged or destroyed, and many students have fled the country with their families. In schools where in-person classes have continued, ongoing airstrikes regularly send students scrambling for shelters.

“The war has a great impact on children,” said Ivan Svarnyk, a historian and educator, “when missiles are flying, when bombs are falling, when their friends are dying, and this is a huge test for the child’s psyche.”

For many, playtime has ended, Mr. Svarnyk added. Others are finding the war makes its way into their games.

Last summer, on the road to Kharkiv, in Ukraine’s northeast, three young children played checkpoint, mimicking blockades set up around the country by the military. During their summer break from school, they stood outside for hours, wearing camouflage and mock uniforms, carrying two knives, binoculars and a toy pistol, and proudly displaying the Ukrainian flag.

Summer camps also offer an escape from the realities of war.

At the Hedgehog’s Camp for the youngest Plast members, children ages 3 to 6 spent a week last August in the forested mountains of the Lviv region. The camp took the children on a woodland adventure through storytelling of Ukrainian folklore and mythology, woven with an appreciation of nature.

The adults running the camp wore costumes depicting characters from these ancient stories, while the children ran through the leafy mountain trails, far from the thoughts of air raid sirens and frontline fighting.

But the war is never really far. Some of the children had been displaced from their homes, forced to flee across the nearby border in Poland and return only sporadically. One of the campers, Marko, 5, attended the camp with his mother, Vira Ihorivna, 33. His father was a volunteer soldier and was killed fighting in the east.

“He understands, but probably as a child, that his father is dead,” Ms. Ihorivna said.

Older scouts must grapple with the idea that they may eventually take the lessons they learn at camp to the front lines.

“I understand that although many people hope that the war will end quickly — you need to believe in the best — but you need to be prepared for everything,” said Ms. Vdovych, the scout at the camp who will return as an instructor.

Out in the forest, where scouts can count only on themselves, she said that lesson on preparedness had been drilled home, along with the idea “We can only count on ourselves.”

“Learning how to build your little life in nature will make it easier in real life,” she said, adding: “There are always challenges. But you learn how to deal with storms and unexpected turns.”

Diego Ibarra Sanchez and Anna Ivanova contributed reporting.

Even the jumps at the Olympic equestrian events were meticulously crafted works of art. In the gardens of the Château de Versailles, riders negotiated fences modeled on the Arc de Triomphe, the Eiffel Tower, Paris bistros, streets with a horse in their name like Passage du Cheval Blanc and a stained-glass window from Notre-Dame.

France, aiming high for the Paris Olympics — perilously high, many thought — was not about to stick mere poles in the ground and ask horses and their riders to jump those obstacles in the former residence of kings.

Uncompromising French ambition has marked the remarkable 16 days of the Olympics, a miracle of detailed planning and execution at a cost of about $4.8 billion. France came into the Games shaken by two rounds of an unexpected legislative election that yielded a political impasse. It will exit with those problems unsolved but with a new self-confidence.

“Today, no responsible politician can say that the French are durably and definitively divided and that there are not possible levers to bring them together,” Gabriel Attal, the departing prime minister, said in an interview.

That appears to be an important change.

Even if political problems flare again in the coming weeks, as they almost certainly will, a core pride at a remarkable accomplishment, impossible without the contribution of all sectors of society, appears likely to endure for a long time.

It is as if the renowned schools of France that produce world-class engineers and world-class analytical thinkers found a way to fuse with the creators of French artistic beauty, turning Paris into a sumptuous, efficient stadium and its sometimes surly inhabitants into some of the kindest people on earth.

Things worked; the party grew; people relaxed. The dismissive French “Bof” and shrug gave way to a universal smile. Paris became a city of cheers and murmurs. Inclusiveness — of French people of every origin, skin color and creed — was a core theme from the opening ceremony onward in a society torn by tense debate over immigration. The embrace extended to visitors from all over the world.

Even the volunteers raking the Olympic beach volleyball court beneath the Eiffel Tower smoothed the sand with a spring in their steps. Nail polish in blue, white and red, the colors of France, was everywhere. France piled up medals, 56 at the latest count, including 14 gold, and found in the swimmer Léon Marchand its hero of the hour, with four gold medal swims.

Abba’s “Dancing Queen” became the national anthem of Sweden as Armand Duplantis soared over 6.25 meters to set a new world record and win the gold medal in the pole vault on Monday. The roar that went up would have taken the roof off the Stade de France if it had one.

The hundreds of “motivators” employed to get crowds going with Gala’s “Freed from Desire” or the Mexican wave were frenzied energizers. They seemed intent on releasing everyone’s inner child. They were also deft. When tensions flared between the Brazilian and Canadian teams in the beach volleyball final, leading to a sharp altercation at the net, the D.J. dissolved the fracas by playing John Lennon’s “Imagine.” The crowd sang. The players smiled.

At other volleyball matches, on sand or not, the motivators had thousands of people intoning, “Monster block! Monster, monster, monster block!!” as spectators raised and lowered their arms to salute the blocking of a spike.

Speaking of things blocked, France still is. Its newly elected Parliament is so divided that it is hard to see how a governing coalition could be formed.

“We don’t really have the culture of coalitions,” Mr. Attal said, alluding to the top-down presidential system that has dominated the Fifth Republic.

The Olympics have been a vacation from that deadlock, but the idyll will not be lasting, and fundamental questions — such as who will run the government — will move front and center soon after the Games end. President Emmanuel Macron, for whom the glow of the Olympics may ease the widespread hostility toward him, will have to name a new prime minister in the coming weeks, even if the August holidays give him a little leeway.

Precedents are not encouraging when it comes to the lingering effect of sporting triumph. The French victory in the World Cup soccer tournament in 2018, a feel-good moment for the nation, was followed within months by the “Yellow Vest” protest movement that brought France to a near standstill.

The famous “black, blanc, beur” (“black, white, Arab”) French soccer team that won the World Cup in 1998 and became the multihued darling of the nation, did not influence France for long enough to prevent Jean-Marie Le Pen, the bigoted leader of the anti-immigrant National Front, from reaching the runoff of the presidential election in 2002.

Still, for now, France is basking in the admiration of the world.

Tony Estanguet, the head of the Paris Olympics Committee, told France Inter radio on Thursday, “These games are still more beautiful in reality than in my craziest dreams. It was worth clinging to this ambitious vision, and it feels good to see the surge of fraternity.”

Left and right, bitterly divided, found a shared patriotism in the success of the Olympics, which had been widely criticized in the prelude as too expensive, too disruptive and simply too ambitious for France to pull off.

“There was an orchestrated drive to detest Paris,” Anne Hidalgo, the Socialist mayor and a driving force behind the Games, told the newspaper Le Monde. “Because Paris is the city of all the liberties.”

Blaming the reactionary right for the destructiveness and negativity in France before the Games, she added: “We should not try to prolong the Olympic moment, we won’t succeed. But we must try to understand and deconstruct what was at work before — that is to say the desire to cast all of humanity into wars of one side against the other.”

At the Parc de la Villette in northeastern Paris, several countries, including France, opened pavilions to celebrate the Games and their national cultures. Crowds in high spirits thronged there day after day.

The India House, with its authentic food, was one major attraction. There I found Esther Benata, 66, a retired actress, and Hélene Castelle, 66, who manufactured leather purses with her husband before retiring.

“We are completely transported!” Ms. Benata said.

“This changes us, and it’s one big party!” Ms. Castelle said. “The Parisians who left town will regret it to the end of their days.”

“The key was all the people, not just French people, mixed together like here, the blending,” Ms. Benata added.

“In September, the usual mess will start over,” Ms. Castelle continued. “That’s certain. But that can’t change the fact we had a great time!”

There have been quibbles — the food at the Olympic Village and the water in the cleaned-up Seine where swimming events were held, for example. There was intense discussion of the color of the track at the Stade de France — was it purple, or pale purple, or pastel purple, or maybe violet, or even periwinkle blue? The jury is still out, but no athletes seem to have complained at this luminous French choice.

France, in the end, proved something to itself and offered something positive to a tense and treacherous world. No Russian athlete competed under the Russian flag. It was Russia’s loss.

“It’s not all over,” Ms. Hidalgo said in her interview with Le Monde, suggesting that pessimism had been overdone.

The 2024 Paris Olympics are almost over. But an end is also a beginning. The last jump at the equestrian events was “LA 28.” At the closing ceremony on Sunday evening at the Stade de France, Ms. Hidalgo will hand the Olympic flag to Karen Bass, the mayor of Los Angeles.

In the predawn hours on a Sunday in late July, members of one of Haiti’s largest armed gangs attacked the town of Ganthier, about 25 miles east of the capital and on a road that the authorities say is used to smuggle weapons.

When police reinforcements arrived in armored vehicles hours later, officers found the streets deserted, the gang members having left after destroying Ganthier’s police station and torturing and killing several residents, according to the town’s mayor and the police.

“The whole town of Ganthier is emptied; there is no one left,” the mayor, Jean Vilonor Victor, told The New York Times.

Weeks after the arrival of a United Nations-backed international security force in Haiti, the gangs who have brought the capital, Port-au-Prince, and other regions in the country to their knees show no signs of letting up.

The international effort to reinforce the Haitian police and a transitional government has alleviated conditions in some sections of Port-au-Prince, experts say, but gang members have refocused their attacks on the outskirts, marauding towns that had escaped their campaign of killings, kidnappings and rape.

The attack on Ganthier, a town of 60,000 people on a major highway linking the capital to the border with the Dominican Republic, is emblematic of the persistent security problem Haiti’s government faces as it tries to rebuild the shattered country, which has seen three years of violence, mass migration and economic ruin.

The first wave of Kenyan police officers to deploy in Haiti as part of the multinational force lacks the numbers or the armaments to dismantle the powerful gangs, experts said.

To make matters worse, three members of the Presidential Transition Council, a governing body that took office in late April, tasked with paving the way for national elections, is under investigation by an anti-corruption government agency over the handing out of government jobs to members of its coalition of political and economic groups.

Council members have denied any wrongdoing.

But Nixon Boumba, a Haitian human rights advocate, said: “Corruption and security go hand in hand. For most of us, the more things change, the more things remain the same.”

The appointment in May of a new prime minister — a respected technocrat, Garry Conille, with experience as a senior United Nations executive — is part of a tricky transition back to democratic rule, with elections scheduled for next year. Haiti has been in turmoil since July 2021, when the last president, Jovenel Moïse, was assassinated in his bedroom.

The arrival of 400 Kenyan police officers this summer was meant to reinforce the beleaguered Haitian police force, which has been fighting a coordinated gang offensive since late February.

For now, the Kenyans are not straying very far from their base, built by U.S. contractors, at Port-au-Prince’s international airport, which reopened to commercial flights in May after being closed for more than two months because of gang violence outside the airfield.

The commander of the Kenyan mission, Godfrey Otunge, said his men were helping bring about a “gradual return to normalcy.”

He claimed credit recently for helping patrol and clear the road to Ganthier, where in a statement he said efforts were underway to “unshackle” the town from gang control.

But Mr. Victor, the mayor, said that security forces left soon after arriving and that gang members quickly returned. “Nobody can go home yet,” said Mr. Victor, who also fled.

A video that circulated recently on social media showed a gang leader in Ganthier wearing a police officer’s cap as an abandoned police vehicle burned in the background.

The Haitian police have helped reduce violence overall in recent months, analysts said. From March to June, at least 1,379 people were killed or injured because of gang violence throughout the country, a 45 percent drop compared with the previous four months, according to the United Nations.

“It’s much quieter in central Port-au-Prince,” said William O’Neill, the United Nations-appointed human rights expert for Haiti.

With Kenyan officers providing support, the Haitian police have entered parts of the capital they had abandoned, said Diego Da Rin, who monitors Haiti for the International Crisis Group.

But large parts of Port-au-Prince, including downtown, are still no-go zones where residents fear to tread and businesses are boarded up. When Mr. Conille, a TV news crew and a heavy police escort went last month to Port-au-Prince’s main public hospital, which has been abandoned because of gang violence, they came under fire and had to make a speedy getaway.

“The government needs to act quickly to reassure the public,” Mr. O’Neill said. “People want to see results more quickly.”

As part of his first moves, Mr. Conille fired Haiti’s police chief and several top commanders, promising bold action to regain control of “all areas controlled by gangs, house by house, district by district and city by city.”

But many Haitians remain unconvinced.

“There are a lot of promises being made but no positive signs of change yet,” said Kesner Pharel, a leading Haitian economist. “The capital is still cut off from the rest of the country by the gangs. They control the roads, and they are still taking territory.”

Mr. Conille, acknowledged in a recent interview with the BBC, that Haiti’s police were “undermanned” and that international support was arriving too slowly.

The United Nations says that over the past year, at least 578,000 people have been displaced by violence, with roughly five million people, nearly half the population, lacking enough food to meet their daily dietary needs.

More than one-fourth of the schools in the Port-au-Prince metropolitan area cannot operate because of the insecurity, according to a recent UNICEF report.

The health care situation in the capital also remains dire, with most hospitals closed after being looted by gangs.

“It’s a catastrophe,” said Dr. Ronald LaRoche, who runs the Jude-Anne Hospital, part of a private health network. “I haven’t even been able to visit our buildings to evaluate the damage. The government surely has good intentions, but they have no power to take on the job.”

Benoit Vasseur leads a Doctors Without Borders team in Haiti with several mobile clinics that often operate in gang-controlled areas. “We see some improvement in security, but it changes from day to day,” he said.

As pressure mounts on the government to take on the gangs, Mr. Vasseur said his medical teams were bracing for even worse mayhem. “We fear we’ll see more patients,” he said.

The new Haitian police chief, Rameau Normil, said in a statement that recent operations had killed 104 “bandits,” a word used to describe gang members.

While the Kenyan reinforcements are welcome, they still number well below the 2,500 personnel that were expected to make up the international contingent. At least six other countries have committed to providing more security forces.

U.S. diplomats say the force’s final size is still unclear because of limited resources on the ground in Haiti, including housing at the Port-au-Prince airport.

But the biggest problem is funding.

“We urge countries to dig much more deeply than they have,” Brian A. Nichols, the U.S. assistant secretary of state for Western Hemisphere affairs, told reporters recently.

The United States has already pledged $360 million of the estimated $600 million annual cost of the deployment, but U.N. authorization for the mission expires in October, and the United States will need to secure Chinese and Russian support to extend it another year.

The Kenyan force is equipped with armored vehicles, but has no air or sea assets, limiting its ability to respond to gang attacks, experts said, adding that the 400 officers already in Haiti need significant beefing up.

“It’s a small force under any account of what is needed,” said Keith Mines, the vice president of the Latin America program at the United States Institute of Peace, who follows Haiti closely.

“It’s a restraint on what they can do,” he added. “We just have to accept that’s what’s there.”

Brazilian investigators on Saturday began analyzing the black boxes from a São Paulo-bound flight to try to understand why the passenger plane fell from 17,000 feet on Friday, in a crash that killed all 62 on board.

But to aviation experts around the world who watched the videos showing the 89-foot plane spinning slowly as it plummeted before crashing almost directly on its belly, the question of what had happened was simple to answer: The plane had stalled.

In other words, the plane’s wings had lost the lift needed to keep the aircraft aloft, causing it to stop flying and start falling.

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An Israeli airstrike early Saturday hit a school compound in northern Gaza where displaced Palestinians were sheltering, killing dozens of people, according to Gazan officials.

The Israeli military acknowledged the attack, but said Hamas and another armed Palestinian group were using the facility for military operations and attacks on Israel.

The strike in Gaza City, the latest in a string of attacks on schools turned into shelters, drew strong condemnation from the European Union and the United Nations, with Josep Borrell Fontelles, the top E.U. diplomat, saying, “There’s no justification for these massacres.”

The strikes have taken place alongside mounting international pressure on Israel to conclude a deal for a cease-fire and an exchange of hostages held in Gaza and Palestinian detainees, with President Biden and the leaders of Egypt and Qatar saying this week that “the time has come.”

The Gaza Civil Defense emergency service said more than 90 people were killed. But that number could not be confirmed, and two doctors at a hospital in the area gave slightly lower totals. Gaza health officials do not distinguish between civilians and combatants when reporting casualties.

The Israeli military did not provide a death toll. But it questioned the Gaza authorities’ statements, saying that its own assessment of the incident was at odds with the reported death toll, and that more than a dozen militants were killed in the strike.

Daniel Hagari, the military’s chief spokesman, said that intelligence gathered by Israel indicated that “no women and children were present” in the building struck by Israeli forces. Regarding the casualty count, he said: “These figures do not distinguish between combatants and noncombatants, and they do not match the information” held by the Israeli military.

The Civil Defense emergency service in Gaza said that the strike hit as more than 200 people gathered before sunrise in a prayer hall to worship. More than 2,000 displaced people had been staying at the shelter, the Al-Tabaeen school in the Al-Daraj neighborhood, the emergency service said.

The attack was launched as the United States, Egypt and Qatar mounted a new effort to restart negotiations for a truce in Gaza next week, with fears rising of an escalation in the conflict between Israel and Iran. Analysts said President Biden and his allies hope the prospect of a cease-fire in Gaza will dampen tensions between Iran, its militant allies and Israel, and put brakes on the momentum toward a regional war.

For days, Israel has tensely awaited retaliation for the assassination of top leaders from Hamas and Hezbollah, both groups backed by Iran. President Biden and the leaders of Egypt and Qatar called Thursday for more talks between Israel and Hamas to end the war in Gaza, saying they would be willing to present a “final bridging proposal” to both sides.

There is “no further time to waste,” the leaders said in a joint statement, a sign of the growing impatience over the stalled peace talks. Hours later, Prime Minister Benjamin Netanyahu of Israel said he would send negotiators to talks next Thursday, while Hamas has yet to respond to the offer.

In Gaza, however, Israel’s campaign — now in its 11th month — dragged on.

At least 17 school buildings have been targeted over the last month, killing at least 163 Palestinians, according to the United Nations. The Israeli military said Hamas has cynically exploited the compounds, and the displaced people sheltering inside, for its own protection; international law experts say Israel needs to do more to avoid harming civilians.

The Israeli military defended Saturday’s attack, saying in a statement that “the strike was carried out using three precise munitions,” and that several steps were taken to mitigate civilian casualties, “including the use of a small warhead, aerial surveillance and intelligence information.” At least 19 militants from the Hamas and Islamic Jihad armed groups were killed in the attack, the statement said.

“The compound, and the mosque that was struck within it, served as an active Hamas and Islamic Jihad military facility,” said Lt. Col. Nadav Shoshani, an Israeli military spokesman, without providing details. He added that the information released by the Gaza authorities in the past has “proven to be sorely unreliable.”

The Gaza Health Ministry’s numbers are believed to be broadly reliable, though there is often uncertainty in the immediate aftermath of specific strikes, and the destruction of the territory’s health system has made tolls harder to track.

Saturday’s airstrike hit two floors, one of which was used for communal prayers and the other for sheltering women and children, a Civil Defense spokesman, Mahmoud Basal, said. He said the prayer hall inside the school complex had been used for worship since the beginning of the 10-month war.

Mr. Basal said 11 children and six women were among those killed in the strike on Saturday, adding that many people were seriously wounded.

Many of those wounded in the Israeli strike, including children, were arriving with severe burns covering much of their bodies, said Tayseer al-Tanna, a surgeon at Al-Ahli Hospital in Gaza City, who called the scene “very difficult to watch.”

Dr. al-Tanna said doctors had been forced to amputate several badly burned and mangled limbs since early morning. They had almost no painkillers to give their patients, he said, and did not have enough time to fully sterilize the already overused equipment between operations.

Fadel Naim, a medical official at Al-Ahli Hospital who served for years as dean of the medical college at the Islamic University of Gaza, widely seen as a Hamas stronghold, said the hospital had received at least 70 bodies since Saturday morning. The strike was followed by a flood of people searching for loved ones missing in the wake of the explosion, he said.

Khamis Elessi, a doctor at the same hospital, in Gaza City, said more than 73 identified bodies were brought to the hospital morgue, along with another 10 who have yet to be identified because they were disfigured in the explosion.

Israeli forces have recently been scaling up military attacks throughout Gaza in areas where they had previously fought Hamas, saying the fighters had regrouped. Hamas has fought a dogged insurgency, resisting Israeli attempts to quash the group. That has raised concerns in Israel that a decisive military victory may be out of reach — even as Gazan civilians continue to face dire conditions.

Troops had previously moved in on the Al-Daraj neighborhood in early July as part of a renewed ground offensive in Gaza City. But the Israeli military appears to have wound down its ground operation there, even as it continued to conduct airstrikes in the area.

The U.N. and other rights organizations have repeatedly said that there is no safe place in Gaza, as areas people are ordered to evacuate to are subsequently targeted by Israeli airstrikes. Almost the entire population of Gaza — more than two million Palestinians — has been displaced, many people multiple times.

Philippe Lazzarini, the head of the U.N. agency for Palestinian refugees, called Saturday’s deadly attack “another day of horror” in Gaza. He called on all sides not to harm civilians or use schools for military purposes.

“It’s time for these horrors unfolding under our watch to end,” he said on social media. “We cannot let the unbearable become a new norm.”

Ameera Harouda and Rawan Sheikh Ahmad contributed reporting.

Russia is pushing back against Ukraine’s largest assault into Russian territory since the start of the war, sending troop reinforcements, establishing strict security measures in border areas and conducting airstrikes, according to the Russian Defense Ministry. One of the strikes on Ukrainian troops involved a thermobaric missile that causes a blast wave and suffocates those in its path, the ministry said.

But even as Russia has halted the quick advances made by Ukrainian troops who launched a surprise cross-border attack five days ago into the southwestern region of Kursk, Ukrainian forces seem to be holding ground. 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.

Pasi Paroinen, an analyst from the Black Bird Group, a Finland-based organization that analyzes satellite imagery and social media content from the battlefield, said in an interview that evidence suggested that Moscow had been able to stall the major advances in Russian territory late in the week.

“We’re now entering the phase where the easy gains have been made,” he said of Ukraine’s initial advance. “This phase, for the first three days, saw the most rapid movement,” he added. “And yesterday, I think, we started to see the effects of the Russian response.”

What all of this means for Ukraine is not yet clear. In the third year of a war that has seemed largely frozen along a 600-mile front line in eastern and southern Ukraine, the decision by Ukrainian forces to cross the border into Russia apparently surprised not just Russia, but also the United States, other Western partners and analysts who spend their days following the war’s troop movements.

Some have speculated that Ukraine hopes to draw Russian troops away from the front lines in Ukraine, giving battle-weary Ukrainian troops a needed rest, although analysts say that has not happened.

But for Russia, the fallout from this past week’s incursion has been a public black eye for President Vladimir V. Putin.

Andrei Gurulyov, a retired military officer who is now a member of Parliament, on Friday condemned Russia’s response and level of preparedness.

“There is no military system in place for guarding the state border, no reserves and no second lines of defense,” he said on Telegram, adding, “If the Ukrainian Armed Forces spent two months preparing for this, how did we miss it?”

Dara Massicot, a senior fellow at the Carnegie Endowment for International Peace in Washington, said that the Ukrainian incursion represented for Russia “a system failure on multiple levels — intelligence, defense and emergency response.”

“Border regions were placed on an emergency footing in 2022 to be specifically postured for these kinds of contingencies,” Ms. Massicot said, “which makes the lapse even more glaring.”

To counter the incursion, Russia’s military appears to be relying mostly on units that were already deployed near the area, according to an analysis by the Institute for the Study of War, a Washington-based think tank. Most of those units consist of military conscripts and irregular forces, as opposed to the battle-hardened soldiers fighting in Ukraine.

Russia’s Defense Ministry said on Friday that it was “continuing to repel” Ukraine’s military. And Alexander Kharchenko, a military correspondent for RIA Novosti, a Russian state-run news agency, said on Saturday on Telegram that while Ukrainian troops had easily entered populated areas in the region days earlier, “now they are met by a dense barrier in front of every village.”

Russian officials and the state news media have repeatedly claimed in recent days to have the situation under control, however, only to then lose more ground.

The new offensive has alarmed the Russian public, and if conscripts are killed, that could bring the war home in a way that losses along the front lines in Ukraine have not.

The conflict also threatens to spill over into neighboring Belarus: On Saturday, Belarus, a Russian ally, said it was sending more troops to protect its border with Ukraine, claiming that Ukrainian drones had violated its airspace during the incursion into Russia. Belarus’s defense minister said on Telegram that its air defense forces had destroyed several Ukrainian drones that violated Belarusian airspace on Friday.

Ukraine has managed to keep much of its troop movements hidden, telling soldiers not to say anything publicly or post any videos. But there have been exceptions, including when a group of soldiers posed in a video outside a facility run by Gazprom, the Russian state-owned gas monopoly, on the outskirts of Sudzha; the video was verified by The New York Times.

Satellite imagery showed several damaged or destroyed buildings in the center of Sudzha, including the office of the public prosecutor and what appears to be an apartment building. The Times reviewed additional satellite imagery that showed fighting continuing as of Friday, with visible smoke plumes and a fire.

Mr. Paroinen said that a few Russian troops were likely still holding out in the center of Sudzha, and that the Ukrainians were trying to set up defenses east of there. But he also said that Ukrainians had encountered stiff resistance when they tried several times to take control of Korenevo, a town about 30 miles to the northwest.

“This may have caused quite a bit of trouble for the Ukrainians,” he said.

Since launching the cross-border attack on Tuesday, Ukrainian officials have said little publicly about it, aside from pointing out that the country’s allies have supported the offensive, at least tacitly.

On Saturday, President Volodymyr Zelensky of Ukraine went further, offering his biggest acknowledgment of the incursion into Russia so far. He referred to the fact that Ukraine had pushed the war “out into our aggressor’s territory” and thanked the military for making it happen.

A day before, Mr. Zelensky obliquely alluded to the offensive and cited one benefit from it: newly captured Russian troops who could be traded for Ukrainian prisoners of war. He expressed gratitude to Ukrainian troops “who are replenishing the ‘exchange fund.’”

“This is extremely important and has been particularly effective over the past three days,” Mr. Zelensky said. “We must return freedom to all our people who remain in Russian captivity.”

Since Russia invaded Ukraine in February 2022, Kyiv’s allies have been wary of any Ukrainian incursions onto Russian soil, fearing that they could provoke Moscow and escalate the war. Matthew Miller, a spokesman for the U.S. State Department, suggested this past week that the Ukrainian incursion did not violate American guidance.

It is not clear whether Russia will redeploy better-equipped forces from the front lines inside Ukraine to suppress Kyiv’s foray into Russian soil. That would take time. It would also relieve pressure on Ukrainian troops who are outnumbered and have been losing ground in eastern and southern Ukraine.

So far, Russian forces have not let up in their frontline pushes. In recent days, they have made some inroads near the embattled eastern Ukrainian towns of Chasiv Yar, Toretsk and Pokrovsk, the Institute for the Study of War said. On Friday, the British Defense Ministry said that Russian troops in the Donetsk region of eastern Ukraine had gained ground, pushing to about 10 miles from Pokrovsk.

After steadily losing ground this year, Ukraine’s success with this latest offensive has buoyed the country’s morale, at least if social media posts are any guide. The head of Ukraine’s Postal Service joked on Telegram that he planned to open a post office in Sudzha.

On Friday, the situation remained tense along the border, with both sides trying to evacuate residents. Russia declared states of enhanced security in the regions of Kursk, Belgorod and Bryansk. It said that would include counterterrorism operations, which allow for restrictive military and security actions inside Russia, as applied to parts of Chechnya for years during the war there.

The Ukrainian authorities, perhaps preparing for retaliation, said on Friday that they were evacuating 20,000 people from the Sumy region, across the border from Kursk.

Reporting was contributed by Anastasia Kuznietsova, Evelina Riabenko, Alina Lobzina and Christoph Koettl, Eric Schmitt and Constant Méheut.

Hundreds of people gathered several days ago outside a detention center known as “Zone 7” in Caracas, the Venezuelan capital, huddled around lists of prisoners, as they clutched plastic bags filled with meals they had packed for the inmates inside.

Eager for information about their detained loved ones, many told remarkably similar stories of sons, daughters and siblings arrested riding motorbikes, walking home from work, coming out of a bakery or stopping by a relative’s house in the days following Venezuela’s disputed presidential election.

They described arrests both sweeping and selective. And no one had been told what criminal charge their relatives faced.

The Venezuelan government has mounted a furious campaign against anyone challenging the declared results of the vote, unleashing a wave of repression that human rights groups say is unlike anything the country has seen in recent decades.

“I have been documenting human rights violations in Venezuela for many years and have seen patterns of repression before,” said Carolina Jiménez Sandoval, president of the Washington Office on Latin America, an advocacy and research organization. “I don’t think I have ever seen this ferocity.”

The country’s autocratic president, Nicolás Maduro, claimed victory in the July 28 election, but the government has yet to provide any vote tallies to support the announcement. The opposition, on the other hand, released tallies showing that its candidate had won in a landslide.

Now, experts say, Mr. Maduro, having seemingly been repudiated by a majority of his constituents, is bent on punishing those he considers disloyal.

“My son grabbed a flag and participated in a protest, but I don’t think he will be convicted for that, will he?” said María Vázquez, 62, a Caracas street vendor who supports the government and urged her son not to protest. “It’s worrisome.”

The Venezuelan government says it has arrested more than 2,000 people for participating in protests disputing the election results.

People were taken both in indiscriminate roundups, amid the protests, and later from their homes in targeted arrests, as the government launched what it called “Operation Knock-Knock,” according to interviews with family members and human rights activists documenting the detentions.

The surge in detentions is particularly alarming, rights groups say, because some arrests came after the president urged his supporters to snitch on their neighbors, using a government app that was supposed to be used to report issues like downed power lines.

“Maximum punishment! Justice!” Mr. Maduro said at a rally last Saturday. “There will be no forgiveness this time!”

The result has been an aggressive crackdown on dissent designed to silence anyone who dares question the election results, human rights activists said.

At least two human rights lawyers are in jail, including one who was arrested when he went to inquire about other detainees. Another activist was taken from the Caracas airport when she tried to leave the country.

When the authorities showed up at the home of María Oropeza, an opposition party leader in Portuguesa, southwest of Caracas, she live-streamed it. “I think first you should show me whether you have a search warrant, no?” she could be heard telling a police officer. “Because this is my home, private property.”

Jordan Sifuentes, the mayor of Mejía, the only opposition mayor in the state of Sucre, in northeast Venezuela, has been held for a week on unknown charges. Mayor José Mosquera of Lagunillas, in Zulia State, was held for six days after being accused of posting a tweet against the government, which he had denied.

Human rights activists and journalists learned in recent days that the government had annulled their passports, effectively trapping them in Venezuela.

People are leaving their houses without their phones, fearing that the authorities will stop them on the street and look at their messages for objectionable content. One man in Zulia was arrested after the police found a meme critical of the elections on his phone, his family said.

“It’s difficult to express in words the intensity and the indiscriminate nature of this wave of arrests,” said Gonzalo Himiob, vice president of the Penal Forum, a human rights organization tracking arrests since the elections.

Though the government claims that more than 2,000 people are in custody, Mr. Himiob said human rights organizations have only been able to document nearly 1,300 people detained.

“Maduro speaks of 2,000 detained, but it doesn’t seem true,” he said. “It seems more like an instruction. He wants to reach that number.”

On July 28, Mr. Maduro faced off against a little-known diplomat named Edmundo González, a stand-in for a more popular opposition leader, María Corina Machado, who had been disqualified by the government from running for office.

About six hours after the polls closed, the elections council announced Mr. Maduro had won another six-year term. Nearly two weeks later, the government has yet to publish any precinct-level elections data proving it.

The tallies collected by opposition observers on election night show Mr. González won by millions of votes.

Spontaneous protests erupted the day after the race, some of which led to clashes between demonstrators, security forces and armed civilian groups that support the government. At least two dozen people were killed, according to human rights groups. Hundreds were arrested.

But arrests continued days after the protests, sometimes on the word of anonymous informers who reported them on VenApp, an app that the government had originally introduced to report public nuisances.

The app has been removed from Google Play and the App Store, but is still available for those who have already downloaded it, according to Amnesty International.

Using civilian supporters to inform on neighbors has echoes of what has happened in Cuba, where the Communist government has long deployed an extensive network of community-based informants.

“Operation Knock-Knock is just beginning,” Douglas Rico, the head of Venezuela’s criminal investigations unit, posted on Instagram. “Report if you have been the target of a physical or virtual hate campaign through social media.”

The government appeared to be employing a “pluralistic” approach to quash dissent, said Ms. Jiménez of the research organization, using all the methods at its disposal, including technology, security forces, intelligence services, armed civilians and the armed forces.

“The array of tools the government is using,” she said, “is something not seen in previous cycles of repression in the country.”

Mr. Maduro insisted that the detained people had participated in an extreme-right fascist plot to oust him. People were paid to burn electoral centers and knock down statues of former President Hugo Chávez, he said, adding that they had confessed to their crimes.

The people who have been arrested will be charged with inciting hatred and terrorism, the government said, and activists said they had been referred to a specialized terrorism court in Caracas. Some of those arrested were caught committing acts of vandalism such as taking down government statues, but many others were merely in the wrong place at the wrong time, civil rights lawyers said.

The attorney general’s office did not respond to a request for comment.

On Thursday, the family of the opposition party leader Américo De Grazia, 64, announced on Instagram that he had been missing for more than 24 hours.

His daughter, María De Grazia, 30, said that after receiving threats on social media, her father, a former mayor and congressman, left his house in Upata and traveled 450 miles to Caracas. After five days there, he suddenly disappeared.

The family learned he was in jail, but said they were not told why.

“They did not come to the house with an arrest warrant,” said Ms. De Grazia, who lives in exile in Houston. “If a family member had not gone looking under rocks for two days, we would still not know where he was.”

The government was clinging to power, she said, by arresting everyone from student leaders to well-known politicians to ordinary citizens. Opposition activists barely stood a chance against such an organized apparatus.

“We are going to war armed with a plastic fork,” she said.

Nayrobis Rodríguez contributed reporting from Sucre, Venezuela, and Sheyla Urdaneta from Maracaibo, Venezuela.