They were lanky and fresh-faced, and the battle they lost had been their first.

Packed into Ukrainian prison cells, dozens of captured Russian conscripts lay on cots or sat on wooden benches, wearing flip-flops and, in one instance, watching cartoons on a television provided by the warden.

In interviews, they recalled abandoning their positions or surrendering as they found themselves facing well-equipped, battle-hardened Ukrainian forces streaming across their border.

“We ran into a birch grove and hid,” said Pvt. Vasily, whose small border fort was overrun on Aug. 6 — at the outset of a Ukrainian incursion into Russia that was the first significant foreign attack on the country since World War II. The New York Times is identifying the prisoners by only their first names and ranks for their safety if they are returned to Russia in a prisoner exchange.

The fighting marked a significant shift in the war, with Ukrainian armored columns rumbling into Russia two and a half years after Russia had launched an all-out invasion of Ukraine.

Russia’s border, it turned out, was defended thinly, largely by young conscripted soldiers who in interviews described surrendering or abandoning their positions. Private Vasily said he had survived by lying in the birch forest near the Russian border for three days, covered in branches and leaves, before deciding to surrender.

“I never thought it would happen,” he said of the Ukrainian attack.

The Russian military command had, by all signs, made the same assumption, manning its border defenses with green conscripts, some drafted only months earlier. Their defeat and descriptions of surrendering in large numbers could increase Ukraine’s leverage in possible settlement talks and lead to prisoner exchanges.

It could also resonate inside Russia. The losses of young, drafted Russian soldiers during wars in Afghanistan and Chechnya stirred widespread discontent at home.

For the bloody trench fighting inside Ukraine, the Russian Army deploys older soldiers mobilized from their civilian jobs, volunteers and prisoners, who agree to a tour of duty in exchange for their freedom, should they survive. Conscripts are barred by law from being deployed outside Russia. But stretched for manpower, or blind to the risk, the military used them to guard the border.

In Russia, conscripts represent the bottom rung in a two-tiered military that took shape in the post-Soviet period. They are drafted after high school and typically serve a year performing menial tasks, like shoveling the snow at bases deep in Russia. Contract soldiers are volunteers, better paid, and they bear the brunt of wars in Syria and Ukraine.

Ukrainian officials say they have captured hundreds of young conscripts over the past week and a half, in what President Volodymyr Zelensky has praised as a move replenishing Ukraine’s “exchange fund” for the swapping of prisoners.

The Ukrainian prison in Sumy, where the conscripts interviewed on Friday were held, has processed 320 prisoners of war so far, 80 percent of them conscripts, according to the prison warden, who asked not to be identified by name for security reasons; the numbers could not be independently verified. After processing, prisoners are sent west, farther from the fighting.

On Friday, the prison held 71 prisoners of war, packed into basement cells, where they are safeguarded from potential airstrikes, the Ukrainian military says.

They wore hand-me-down track suits, T-shirts and shorts that their captors had provided. Some had shrapnel or gunshot wounds. Wide-eyed, and appearing to be disoriented, they watched as guards escorted journalists into the cells for interviews.

The prison provided access for several media outlets, including The Times, whose journalists identified themselves, and asked permission for interviews and to take photographs. The detainees were interviewed after being captured, and in the presence of guards, so their accounts could not be independently verified. The guards did not intervene, and were some distance from the prisoners during the conversations.

The prisoners described being stationed at platoon strength, about 30 men, in concrete or earthwork fortifications spaced a mile or so apart along the border. There, they had faced a sudden, ferocious attack and quickly gave up the fight.

Ukrainian soldiers, independent military analysts and Russian military bloggers have also reported a quick rout along the border.

Pvt. Igor, a slender 21-year-old who was drafted in December, said Ukrainian artillery fire had picked up a few days before the incursion. “We reported to commanders, but they didn’t react,” he said. “They said, ‘Well, there’s nothing we can do about it.’”

On the day of the attack, bombarded by artillery, he tried to hunker down in the fortification, but it caught fire.

He and others ran for a nearby forest, he said. From his group of 12 who had tried to dash to safety, five survived, he said.

The position had only one recoilless rifle, he said, and it could not shoot at Ukraine’s American-provided Bradley infantry fighting vehicles as they attacked because it was pointed in the wrong direction.

Pvt. Sergei 20, from the region of Tatarstan in the Volga River valley, said his platoon leader had led the 28 soldiers from his fort on a chaotic retreat. They holed up in a village house, but Ukrainian soldiers found them. All surrendered.

The platoon leader, he said, had yelled out a window: “‘There are conscripts here. We want to surrender.’”

Some lamented being sent with inadequate training to a battlefield that has evolved into a complex mixture of exploding drones, electronic jamming and the use of finely honed tactics for storming trenches and fortifications.

Pvt. Dmitry 21, from the Komi region in northern Russia, said that when their radios stopped working on the day of the attack, he assumed it was because of Ukrainian jamming. Without orders, the soldiers realized they were overmatched and tried to retreat, but were captured. “They said we might see a sabotage group, maybe 10 guys, not an army,” he said.

While the Ukrainian forces took full advantage of the element of surprise and what both sides described as a weak and disoriented Russian defense, the Ukrainian advance has bogged down away from the border against better prepared Russian forces.

Conscripts are still being caught, however. This past week, the Ukrainian news media published a video said to show more than 100 conscripts lying face down in a field, reportedly filmed by the S.B.U., Ukraine’s domestic intelligence agency. The videos could not be independently verified.

For Mr. Zelensky, the influx of prisoners of war eases what had become a simmering domestic problem. The distraught families of Ukrainian soldiers held in Russia have staged weekly protests in Kyiv, the capital, to draw attention to their detained loved ones. Russia does not disclose the numbers of Ukrainians it has captured, but was assumed, before the incursion, to have more Ukrainians than Ukraine had Russians.

The haul of new prisoners has cheered these families.

Tetyana Vyshnyak, whose son served with the Azov regiment, was captured and sentenced to 22 years in a Russian prison. There had been little hope of his release, given Russia’s advantage in the number of prisoners of war.

“For all of us, this is a great chance and hope that our loved ones will be exchanged,” Ms. Vyshnyak said in an interview.

Valeria Subotina, a former press officer with the Azov regiment, spent 11 months in Russian captivity before an exchange in 2023. “It’s incredibly difficult to go on living when your friends and loved ones are in captivity,” she said. “I hope the operation in the Kursk region can change this.”

Yurii Shyvala contributed reporting from Sumy, and Stas Kozljuk from Kyiv, Ukraine.

The war in Gaza had barely begun when 9-year-old Khaled Joudeh suffered an unimaginable loss. His mother, father, older brother and baby sister, along with dozens of other relatives, were all killed in an Israeli airstrike on their home.

In the months that followed, Khaled tried to be brave, his uncle, Mohammad Faris, recalled. He would comfort his younger brother Tamer, who, like Khaled, had survived the Oct. 22 strike that killed their family. But Tamer, 7, was left badly injured with a broken back and a broken leg, and was in constant pain.

“He would always quiet his brother when he cried,” Mr. Faris told The New York Times in a recent phone interview. “He would tell him: ‘Mama and Baba are in heaven. Mama and Baba would be sad if they knew we were crying because of them.’”

At night, when the unrelenting Israeli airstrikes on Gaza would start up again, Khaled would wake up shaking and screaming himself, sometimes running to his uncle to seek comfort.

It was a short and terrifying existence for the young brothers that ended when another airstrike hit the family home where they were sheltering on Jan. 9, killing Khaled, Tamer, their 2-year-old cousin, Nada, and three other relatives, according to two family members.

Their story epitomizes how the 10-month-old Israeli war in Gaza has taken an exceptional toll on children, who are caught in the middle of the conflict.

After the Oct. 7 Hamas-led attack on Israel, the Israeli military launched the war with the stated aim of eradicating Hamas, unleashing one of the heaviest aerial bombardments the world has seen in this century on densely populated Gaza. Israel has accused Hamas of taking advantage of Gaza’s urban terrain to provide its fighters and weapons infrastructure with an extra layer of protection, running tunnels under neighborhoods, launching rockets near civilian homes and holding hostages in city centers.

Hamas denies these accusations and says its members are Gazans themselves and live among the population.

International law experts have said that Israel has a responsibility to protect civilians, even if Hamas exploits them the way Israel says it does. The Israeli military says it takes “all feasible precautions” to mitigate harm to civilians.

The children of Gaza have suffered in myriad ways. Of the tens of thousands of Palestinians killed in the war, an estimated 15,000 were under 18, according to Gazan health officials. The United Nations estimates that at least 19,000 more children have been orphaned. And nearly one million children have been displaced, according to UNICEF, the U.N. children’s agency.

“Gaza remains the most dangerous place in the world for children,” said Jonathan Crickx, a spokesman for UNICEF.

Most children are living in overcrowded homes where multiple families shelter together, or in ramshackle tents that can feel like ovens in the summer heat, lacking both running water and sanitation. Thousands are severely malnourished and at risk of dying of hunger.

The United Nations called on Friday for a weeklong cease-fire in Gaza to allow vaccinations to prevent an outbreak of polio, saying many children were at risk. The same day, the first case of polio in the enclave in many years was confirmed by the Gaza health ministry.

It has been a constant struggle just to survive in Gaza, and children have had to help out.

When he visited the territory a few months ago, Mr. Crickx said, he rarely saw children playing or laughing. Instead, he mostly saw them helping their families: carrying jugs of water from filling stations, trying to find food, and helping to move their few belongings when the family was displaced.

Mr. Crickx said he had seen a boy on the street who appeared to be no older than about 5, pushing a wheelchair with two jerrycans, which he had filled with water, resting on the seat. The handles of the wheelchair were higher than the top of the boy’s head and he could barely see where he was going.

“There is no childhood in Gaza,” Louise Wateridge, a spokeswoman for the main U.N. agency that aids Palestinians, UNRWA, wrote on social media last month. “Malnourished, exhausted. Sleeping in rubble or under plastic sheeting. Same clothing for 9 months. Education has been replaced by fear & loss. Loss of life, home & stability,” she added.

Throughout the war, parents have gone to extraordinary lengths to try to protect their children.

They scrawl their children’s names directly onto their skin to identify them if they are lost, orphaned or killed. At morgues, burial shrouds are cut into smaller pieces to wrap the youngest victims. Sometimes, children’s bodies are wrapped in the same shroud as their parents, laid to rest on the chest of their mother or father.

Some parents quietly say that if their child is killed, they hope they will at least die in one piece and have someone to bury them.

In the first weeks of the conflict, families began planning for the worst. Khaled’s father told his relatives that if any of them were killed, those who survived must protect and educate the children, Mr. Faris said.

Not long after that, on Oct. 22, an Israeli airstrike destroyed two buildings where Khaled’s extended family was living in the town of Deir al-Balah, in central Gaza, according to relatives and local journalists.

Khaled and Tamer were the only ones in their immediate family to survive. Nada, their 2-year-old cousin, was the sole survivor of that first strike from her own immediate family.

Just after the October strike, in the courtyard of the morgue where dozens of shrouded bodies were laid out on the ground, Khaled, barefoot and crying, kissed the faces of his parents and siblings a final, sorrowful farewell.

A total of 68 members of Khaled’s extended family were killed that day as they slept in their beds, according to accounts at the time from three of the boy’s relatives. They were laid to rest together, side by side, in a mass grave.

For nearly a month after their parents were killed, Khaled and Tamer stayed with their uncle, Mr. Faris, in another family building in Deir al-Balah. Khaled, Tamer and Nada would occasionally venture out to play in the rubble-lined street.

“They are kids and would try to hold on to their childhood,” Mr. Faris said. “They would play outside at certain points of calm. But then airstrikes would often send them back screaming,” he added.

“He would come quickly and hide near me,” Mr. Faris said of Khaled.

Then, on Jan. 9, Khaled’s all-too-short life came to an end.

About 2 a.m., as the family slept, an Israeli airstrike hit the home where they were sheltering, according to Mr. Faris and another relative, Yasmeen Joudeh, 36. Khaled, Tamer and Nada were killed, along with two uncles and their grandfather.

The body of the grandfather, who had recently returned to live with them, was found in the street. He had survived long enough to stagger out of the bombed building, cradling Nada’s body in his arms, said Ms. Joudeh, who was in Egypt at the time and heard the details from relatives in Gaza later.

The Times learned of Khaled’s death months afterward.

When asked about the strikes on the Joudeh family homes in October and January, the Israeli military did not provide a reason.

Regarding the October attack, the military said only that it could not address questions about a strike on this family.

After the January strike, The Times gave the military the date, time and street location. But the military said The Times “did not provide the I.D.F. with enough information in order to properly look into the alleged strike,” and asked for the coordinates to pinpoint the location of the building that was hit.

Mr. Faris said that his extended family was not associated with any of the Palestinian armed groups that Israel says it has been targeting in the war in Gaza.

“They had nothing to do with anything,” he said.

Like other members of their family — and so many other Gazans since — the three children, their grandfather and the two uncles were buried together in an unmarked grave.

Samar Abu Elouf contributed reporting.

While he can’t turn water into wine, Nigel Braun is making vodka out of thin air.

He is neither miracle worker nor magician. His secret is chemistry, and he films his experiments inside a commercial-grade laboratory in Montreal and shares the videos on his YouTube channel. That’s where 6.5 million subscribers know him as NileRed, like the fluorescent chemical dye, a name he acknowledges sounds vaguely biblical.

Mr. Braun’s videos surged in popularity during the pandemic, reaching 2.5 billion views, and as his audience ballooned, so did his ambitions. His experiments — often whimsical, sometimes practical and occasionally dangerous — range from transforming paint thinner into cherry cola, to developing bulletproof wood, to making carcinogens from scratch.

Over the past decade, since dropping out of grad school, Mr. Braun, 32, has outgrown a hobby workshop in his parents’ garage and two other facilities, settling into a third lab large enough to rival some academic research spaces in Canada.

But Mr. Braun considers himself less a chemist or a science communicator in the vein of Bill Nye and MythBusters than an adventurer. “I want to have a journey,” he said. “I’m not interested in just conveying information.”

Part of his appeal is that he doesn’t care to make chemistry look easy or neat.

Some of the tasks he sets himself on are both epic and arduous, like his many attempts to make purple gold, an alloy of gold and aluminum that gives the metal a unique color, but whose recipe is only vaguely described in one line of ingredients in a patent.

With no other information to draw on, the process to make purple gold was riddled with trial and error and was one of the most frustrating projects he has ever worked on, Mr. Braun told his viewers in a December 2023 video. But he ultimately succeeded, making a ring. It is probably one of the few pieces made entirely of purple gold to exist, he said, because the metal is as brittle as glass.

“Doing the science allows you to have something that you literally can’t buy,” he said, seated in his lab, where a display case holds a selection of the items he has made, including a knife beautified by bismuth crystals, a bouncy metal known as metallic glass and an ultra lightweight material, aerogel, used in space research.

The NileRed videos defy the conventional wisdom of staying relevant online by keeping it short. Mr. Braun’s latest videos tend to be about an hour long, and he publishes them infrequently — violating another rule of social media success — because of the extended timeline on his complicated undertakings.

But the lab is buzzing year-round. Thanks to the advertising and other income he brings in across all of his social media platforms — with 18 million followers and subscribers in total — his company makes a couple million Canadian dollars a year. He has hired two friends and two family members to help.

Mr. Braun’s lab is full of premium equipment and NileRed branded beakers, a far cry from his early days when he scavenged the broken glassware bin in the lab at McGill University for supplies he could repurpose.

A large container that creates an inert atmosphere for testing substances is rigged with cameras. An isostatic press can crush objects with a force like the ocean depths. He recently acquired a type of magnetic press so enormous it caused a forklift to tip.

Mr. Braun likes to use all of this top-end equipment to design experiments that take unexpected twists.

After reading an article about reducing global warming by transforming carbon dioxide into biofuels, he realized that by pulling CO2 and water from the air — and then using the water to make hydrogen — he had the basic ingredients to make ethanol, like the alcohol found in vodka.

An office joke about getting drunk on global warming birthed a vodka-from-air experiment that now occupies a lab bench covered in a maze of tubing, machines, tanks and pressure gauges. For those whose taste in alcohol runs elsewhere, Mr. Braun has also made toilet paper moonshine.

One danger of hobby chemistry — especially in a post-“Breaking Bad” world — is being suspected of using one’s powers for criminal pursuits.

Distilling alcohol for research is legal in Quebec, and Mr. Braun has so far received only one call from the Canadian police. They contacted him after his purchase of a large filter — sometimes used to make illegal drugs — was flagged by customs. But his scientific explanation put the officer at ease.

Still, sometimes he knowingly makes his experiments sound vaguely sketchy.

“Today, I’ve decided to make some fresh, powdered ‘coke,’” Mr. Braun said into the camera on a recent shoot.

After reeling in viewers with a hint that some cocaine production might be in the offing, he eventually revealed that the white powder he had in mind would be produced from the bottle of Coca-Cola he had kept concealed in a back pocket. The Coke was from Mexico, where the drink is made not with high-fructose corn syrup as it is in the United States, but with cane sugar — which is what his experiment would extract.

Based on stories he has heard from peers in the United States, Mr. Braun is not confident that all NileRed experiments would be strictly legal there. It’s one other reason he doesn’t want to relocate south of the border, despite the pull Hollywood has on YouTube stars who strike it big.

But an even more important draw to staying in Montreal: his family. Mr. Braun’s younger brother, Corey, helps manage the channel and his mother, Jody Tanaka, assists with administration. Dorian Braun, his father, helped get him started by yielding some garage space to provide the original backdrop of NileRed videos.

“It was an open workshop,” said the elder Mr. Braun, a sound engineer and retired college professor. “That means that every knucklehead kid on the street is over here, making bows and arrows and contraptions.”

When experiments went wrong — the tear gas incident comes to mind, to say nothing of the time acid vapors ate into some metal tools or the (minor) lithium explosion — the father would let out an exasperated sigh, but generally not stifle his son’s creativity.

The younger Mr. Braun majored in biochemistry during his bachelor’s studies at McGill, but he abandoned his graduate degree and his work as a lab technician after having a sudden realization about his life’s path.

“I remember this moment that hit me: Why am I doing chemistry for someone else all day when I could just do chemistry for myself?” he said.

In contrast to the protracted gaps between check-ins with his academic supervisor as a grad student, the gratification and feedback from Mr. Braun’s audience is almost immediate when he posts a video.

“I try to watch it as soon as humanly possible,” said Chenxin Li, a NileRed subscriber and molecular biology research scientist who has faced the challenge of keeping his students at the University of Georgia engaged in science.

“His channel has the perfect answer: It’s the sense of curiosity or a sense of wonder,” Mr. Li said. “That is important, especially if you run a YouTube channel, because the world’s most entertaining content is a few clicks away.”

As a scientist, Manfred Ehresmann, a space systems researcher at the University of Stuttgart in Germany, envies Mr. Braun’s freedom to take his curiosity in any direction, unencumbered by bureaucracy or the need of writing grant applications.

“If you see someone like NileRed doing it by himself, it’s a kind of inspiration,” Mr. Ehresmann said.

In future videos, Mr. Braun wants to focus on innovative materials, perhaps with an application in the burgeoning space economy.

“Science is only interesting because it’s useful,” Mr. Braun said. “If it’s not useful, it’s just a bunch of party tricks.”

An Israeli airstrike hit a factory in a small town in southern Lebanon, killing at least 10 civilians, Lebanese officials said on Saturday, as people across the Middle East uneasily awaited reprisals against Israel by Iran and its allies for a pair of assassinations.

Israel’s military said it had targeted a weapons warehouse used by Hezbollah, the Iran-backed Lebanese militant group, in the strike overnight on Friday. But the mayor of the town of Toul, where the attack took place, disputed that account.

The strike appeared to have destroyed the factory and an adjacent structure that were inhabited by Syrian refugees who worked there, as well as their families. Reporters who visited the site saw steel beams but no signs of weaponry.

The mayor of Toul, Saeed Mahmoud, said in a phone interview that the factory was used to collect steel spare parts.

The death toll was one of the largest so far in Lebanon amid the near-daily exchange of border attacks with Israel in the 10 months since the war in Gaza began. Hezbollah fighters and other Iran-backed militants have been attacking Israel in solidarity with the Palestinians in Gaza, leading to months of cross-border fire by both sides.

The tensions have escalated sharply in recent weeks following the killings of Fuad Shukr, a senior commander in Hezbollah, and Ismail Haniyeh, a top leader of Hamas, groups allied with Iran. Hezbollah and Iran have vowed to retaliate more forcefully than before against Israel, leaving the Middle East on tenterhooks for more than two weeks.

The Biden administration has led a renewed diplomatic push for a Gaza cease-fire, which U.S. and regional officials hope will prompt Iran and its allies to curb any retaliation and avert a wider regional war. Secretary of State Antony J. Blinken was scheduled to travel to Israel on Saturday to help facilitate the talks, which are being mediated by the United States, Egypt and Qatar.

On Saturday, Israel’s cease-fire negotiations team briefed Benjamin Netanyahu, the Israeli prime minister, on two days of talks in Qatar that ended on Friday. The security chiefs who participated in the negotiations expressed “cautious optimism” about the ability to move toward an agreement, Mr. Netanyahu’s office said in a statement.

All of the people killed in the strike on Toul, near the southern city of Nabatiye, were Syrian refugees and included a woman and her two children, said the Lebanese health minister, Dr. Firass Abiad.

More than a million Syrian refugees fled to Lebanon to escape a long-running civil war at home that began in 2011. Syrian laborers often live with their families where they work.

On Saturday afternoon, Israeli drones circled above the remnants of the destroyed factory. Next door, a collapsed concrete building held what appeared to be the sleeping quarters of the workers and their families. The broken concrete and the metal rebar that once supported the structure were strewed with clothing and the broken plastic of a child’s car seat.

One laborer was killed where he was sleeping along with his wife and two children, according to rescue workers who dug them out of the rubble. At least six other laborers were killed in the strike and two were wounded, the rescue workers said.

The Israeli military said it was looking into the claim that civilians were harmed in the attack.

Hezbollah’s chief, Hassan Nasrallah, threatened in July to hit new targets in Israel if it continued to target civilians in Lebanon. In response to the latest attack, Hezbollah said it fired a barrage of rockets at Ayelet Hashachar, a kibbutz in northern Israel.

The Israeli military said roughly 55 rockets crossed into Israeli territory, some of which ignited fires. There were no immediate reports of casualties. An Israeli soldier was severely wounded in a separate rocket attack from Lebanon on Saturday morning, the military said.

For months, Israel and Lebanon have appeared to carefully calibrate their attacks in an attempt to avoid a wider escalation.

Hezbollah has fired thousands of rockets and drones at northern Israel in solidarity with Hamas, which led the massive surprise attack on Israel on Oct. 7 that set off the war in Gaza.

Israel has responded to attacks from Lebanon with bombardments that have killed more than 500 people, most of them Hezbollah fighters, according to figures from the Lebanese health ministry, Hezbollah and the United Nations.

But after a rocket attack from Lebanon in late July that killed 12 children and teenagers in the Israeli-controlled Golan Heights, Israel killed Mr. Shukr, one of Hezbollah’s highest-ranking military commanders, in an apartment in the southern suburbs of Beirut.

Hours later, an explosion widely attributed to Israel killed Mr. Haniyeh, the leader of Hamas’s political bureau, who was staying in a closely guarded state guesthouse in the Iranian capital, Tehran, to attend the inauguration of a new Iranian president. Israel never publicly confirmed its involvement.

Iran and its ally Hezbollah have pledged to avenge the killings. But U.S., Iranian and Israeli officials said on Friday that Iran had decided to delay any reprisals against Israel to allow mediators to continue working toward a cease-fire in Gaza.

High-level talks in Qatar on a truce and the release of the 115 hostages still held by Hamas and its allies in Gaza ended without an immediate breakthrough on Friday. But the United States, Egypt and Qatar said the negotiations would go on next week in Cairo, as mediators raced to try to secure a deal.

Even as senior officials have shuttled from capital to capital in an attempt to end the war, the fighting in Gaza has gone on. About 15 members of a single family, including children, were killed when their house was bombarded, according to the Palestinian civil defense agency.

Israeli aircraft struck dozens of sites across the Gaza Strip over the past 24 hours, the Israeli military said on Saturday, and ground troops swept through parts of the southern city of Khan Younis, already devastated in an earlier assault.

The Israeli military again ordered Palestinians to flee parts of central Gaza that Israel had previously designated a “humanitarian zone” for many of the nearly two million Gazans who have been displaced during the war.

Avichay Adraee, an Israeli military spokesman, said Hamas and other militant groups had repeatedly fired rockets from the area.

Many Gazans have been displaced multiple times by the war. Aid groups say there is still nowhere safe for them to go, as Israel has vowed to target Hamas wherever it believes the organization is operating.

“Many of the thousands of families affected only recently arrived in the area, after other displacement orders in Khan Younis,” said Louise Wateridge, a spokeswoman for the U.N. agency that aids Palestinian refugees.

Gazans are “trapped in an endless nightmare,” she said.

Hwaida Saad, Victoria Kim and Raja Abdulrahim contributed reporting.

Ever since the Korean War was halted in an uneasy truce in 1953, South Koreans have lived under an American promise to defend their country, if necessary, with nuclear weapons. President Biden emphatically reiterated that commitment last year, vowing that any nuclear attack by North Korea would lead to the destruction of its government.

But decades of American assurances have failed to deter North Korea from building a nuclear arsenal and then expanding it. Led by Kim Jong-un, North Korea has also become more provocative, testing missiles powerful enough to reach the United States. And it has rattled South Korea by reviving a Cold War-era defense agreement with Russia, another nuclear-armed state.

The South has long considered it a taboo to pursue atomic weapons in defiance of Washington’s nonproliferation policy. But jitters about security here have been intensified by the possible re-election of former President Donald J. Trump, whose commitment to the alliance between Washington and Seoul appears to be shaky at best.

Now, a growing majority of South Koreans say their country needs its own nuclear weapons instead of relying on the United States for protection. The idea, although still disavowed by the South Korean government, is increasingly becoming part of mainstream political debate.

Polls show that many South Koreans say they can no longer trust the American nuclear umbrella to guard them from North Korea. They doubt that Washington would come to their aid in the event of a conflict with North Korea now that Pyongyang is racing to develop the ability to attack American cities with nuclear warheads.

“We cannot expect — and should not ask — the American president to use his nuclear weapons to defend an ally at the risk of sacrificing his own people,” said Cheong Seong-chang, who leads a group of 50 analysts pushing for a domestic nuclear arsenal in South Korea. “We must defend ourselves with our own.”

South Korea abandoned its nuclear weapons program in the 1970s, as Washington pushed nonproliferation, and chose to rely on the United States to defend it against the North. Tens of thousands of American troops have been garrisoned for decades in the South, which for many years also hosted U.S. nuclear weapons. Washington withdrew those arms in 1991, hoping the disarmament would incentivize Pyongyang to stop pursuing its own nuclear weapons.

For a while, Washington had two important partners in that effort: China and Russia. But in recent years, it has found itself increasingly at odds with both of those countries on issues such as trade tariffs and the war in Ukraine. Now, neither cooperates in American-led efforts to roll back North Korea’s nuclear ambitions.

Mr. Kim’s regime has tested both atomic weapons and intercontinental ballistic missiles. It is developing technology to deliver multiple nuclear warheads with a single missile. It is also escalating its threat to target South Korea with a fleet of nuclear-capable, short-range ballistic missiles, which Mr. Kim said this month he would deploy near the border with South Korea.

In June, the Stockholm International Peace Research Institute estimated that North Korea had built roughly 50 nuclear warheads and had enough fissile material to build another 40 or so. It was also focusing on tactical nuclear weapons, which have a smaller payload.

“There is a growing concern that North Korea might intend to use these weapons very early in a conflict,” wrote Matt Korda, a researcher at the institute.

It was fears such as these that President Yoon Suk Yeol of South Korea tried to address when he met Mr. Biden at the White House last year. The two leaders deepened their alliance and signed the Washington Declaration to show that the American defense commitment was ironclad. Last month, they reaffirmed that any nuclear attack by North Korea would be met with “a swift, overwhelming and decisive response.”

“For the first time, it has been written down in a document that American nuclear assets will be tasked with deterring and countering North Korea’s nuclear force,” said Kim Tae-hyo, Mr. Yoon’s deputy national security adviser.

But that has done little to tamp down misgivings in South Korea about the American nuclear umbrella, which also covers Japan.

A poll in February showed that the percentage of respondents who said Washington would defend their country with nuclear weapons even though North Korea could attack the mainland United States with nuclear missiles had dropped to 39 percent from 51 percent last year. Another survey, which has been conducted annually for a decade, found a historical shift. Asked to choose between having nuclear weapons or U.S. troops on their soil, more South Koreans, for the first time, picked the former.

Other surveys have found as many as 70 percent of all South Koreans supporting an independent nuclear arsenal. It has become increasingly common for conservative politicians and private and government analysts to support or discuss the idea, especially after Russia’s invasion of Ukraine highlighted the extent to which a nuclear-armed power could get away with invading a nonnuclear neighbor.

“The call for nuclear weapons will be anything but short-lived because ‘going nuclear’ sounds sexy as a slogan,” said Lee Byong-chul, who has studied nuclear nonproliferation at the Institute for Far Eastern Studies in Seoul. “But there is a huge gulf between high public support and a lack of technical capabilities and political intention to build nuclear weapons.”

South Korea has neither facilities to produce fuel for nuclear bombs nor the technical know-how to design nuclear weapons. And while Mr. Yoon has been more antagonistic toward the North than his recent predecessors and briefly warmed to the idea of going nuclear, there is little political will in the South to pursue atomic weapons.

Strengthening reconnaissance and missile abilities, analysts say, would serve South Korea better and give it the ability to launch pre-emptive strikes against the North.

Building nuclear weapons would be “redundant” and “would not make South Korea any safer,” said Chun Yung-woo, a former national security adviser, “as long as the South Korea-U.S. alliance is alive and well.”

But the future of that alliance is likely to be volatile if Mr. Trump — who tried to negotiate with Mr. Kim face to face — is re-elected in November.

“It’s nice to get along when somebody has a lot of nuclear weapons,” Mr. Trump said of Mr. Kim when he accepted his party’s presidential nomination last month. “I think he misses me, if you want to know the truth.”

For supporters of a domestic nuclear force in South Korea, Mr. Trump’s potential return to power could be a good thing. He once said he would be open to allowing Japan and South Korea to build their own nuclear arsenals rather than depend on the American nuclear umbrella.

“It could open a window of opportunity,” said Mr. Cheong, the pro-nuclear analyst.

The success of Ukraine’s secret incursion into Russia is clear. Ukrainian forces pushed past two lines of Russian defenses in the southwestern region of Kursk and moved through Russian highways and villages with little resistance. Since the operation began 11 days ago, they have gone beyond Kursk to the neighboring region of Belgorod, putting other communities on edge and rattling Moscow.

The ultimate strategy and goals of the invasion, though, are still murky. Western allies, including the United States and Germany, say they are watching and monitoring the situation but letting Ukraine lead the way. Even the Ukrainian leadership seems surprised by the extent of the operation’s initial success, the first time that Russia, a nuclear power, has been invaded since World War II.

So now what?

Ukraine has several options.

Ukrainian forces could try to keep pushing further into Russia. They could dig into the territory they now hold and try to defend it. Or, battered by continual losses in eastern Ukraine, especially this week near the strategically important city of Pokrovsk, they could decide that they have made the point to the West, and to Moscow, that Russia is not invincible. In that case, they could then pull back.

“We are playing here a bit on the psychological point that great powers do not lose their territories,” said Mykola Bielieskov, a senior analyst from Come Back Alive, a foundation that provides support to members of Ukraine’s military. If Russia loses, “it means that they are not that big.”

There are vulnerabilities for both sides.

Ukrainian officials have told senior United States civilian and military officials that the operation aims to create an operational dilemma for the Russians — to force Moscow to divert troops off the front lines in the eastern Ukraine region of Donetsk, where they have made slow but steady progress for weeks.

John Kirby, the U.S. National Security Council spokesman, said in an interview with MSNBC on Thursday that Russia had begun deploying its forces to Kursk, although he did not specify where they were coming from. He declined to give an assessment of the Ukrainian operation in Kursk, but said the United States was monitoring how Russia is reacting and redeploying its troops.

“In the meantime, we are going to continue to make sure that Ukraine has the weapons and capabilities that it needs to defend itself,” Mr. Kirby said. “We are going to continue to talk to Ukrainians.”

But the operation has also created a vulnerability for Kyiv. Some of its valuable, battle-hardened soldiers from the 600-mile front line in eastern and southern Ukraine have moved to Kursk. And that has weakened its positions in eastern Ukraine.

By Aug. 9, four days into the Russian incursion, Russian forces had pushed to about 10 miles outside the beleaguered eastern Ukrainian town of Pokrovsk, a critical logistics hub for Ukrainian forces, according to Britain’s Defense Ministry. Russian forces have been hitting them along this stretch of the Donetsk region for months.

By Thursday, the situation was even worse. Residents of Pokrovsk, about 40,000 people, were urged to leave — the Russian Army was about eight miles from the city.

The Institute for the Study of War, a Washington-based think tank, said on Thursday that Russian troops had also made gains toward the frontline town of Toretsk, whose capture would ease the way for Russian forces in the Donetsk region of eastern Ukraine.

Ukraine, it appears, wants to hold ground.

So far, the Ukrainians have not talked publicly about their plans in Russian territory. Gen. Oleksandr Syrsky, who took over as Ukraine’s top military commander in February, claimed on Thursday that his troops had pushed more than 21 miles into Russia. He said that Ukraine controlled more than 80 Russian settlements in the Kursk region, including Sudzha, a town of 6,000. The claims could not be independently verified, although analysts say that Sudzha is likely under full Ukrainian control.

Fighting has also expanded to the neighboring regions of Belgorod and Bryansk, where Russia has introduced counterterrorism measures.

As Ukrainian soldiers make inroads into Russia, the leadership appears to be making plans to hold ground, analysts say.

Mr. Syrsky said on Thursday that Ukraine had set up its first military office in Kursk. A deputy prime minister talked about creating a humanitarian corridor extending from the Kursk region south to the Ukrainian border region of Sumy. At a Wednesday meeting, President Volodymyr Zelensky said that Ukrainian troops were protecting Russian citizens and following the rules of international law.

Ukraine is nimble, but Russia is bigger.

So far, Ukrainian troops do not seem to be building the kind of entrenched lines seen in eastern Ukraine, where trenches, anti-armored vehicle ditches and anti-tank pyramid obstacles known as dragon’s teeth dot the landscape.

Such digging in presents risks, said Serhii Kuzan, the chairman of the Ukrainian Security and Cooperation Center, a nongovernmental research group.

Any fixed position would be exposed to potentially devastating Russian airstrikes and would be difficult to defend against Russian troops attacking from different sides. Russia, after all, has the upper hand in forces and weapons.

Mr. Kuzan said Ukraine should instead continue to execute what he called “highly maneuverable combat operations,” by attacking where Russia does not expect and performing raids with small units to probe and destabilize Russian defenses.

“We cannot fight a symmetrical war — tank against tank, soldier against soldier — because the Russians have greater numbers of forces,” Mr. Kuzan said.

Ukraine has not faced much resistance from Russian forces at this point. Moscow has been slow to mount a major defense and has not yet successfully countered Ukrainian troops in Kursk, analysts say. Russian military bloggers, though, claimed that Ukrainian forces were advancing at a slower tempo on Thursday.

The gains in Russia could provide negotiating leverage.

Analysts say the Ukrainians could also use the territory as a kind of bargaining chip with Russia, if they manage to hold it. Ukrainian officials have told Washington that Kyiv wants leverage for the future, according to U.S. officials, perhaps to swap the Russian territory for land near Kharkiv that Russian forces took in the spring.

Mykhailo Podolyak, a top Ukrainian presidential adviser, said on Friday that Russia would be forced to the negotiating table only through suffering “significant tactical defeats.”

“In the Kursk region, we can clearly see how the military tool is being used objectively to persuade” Russia to enter “a fair negotiation process,” he wrote on social media.

Ukraine also claims to have captured hundreds of Russian prisoners of war, who could be traded for Ukrainian prisoners held by Russia. The Russians guarding the border posts in Kursk were mostly conscripts, forced to serve as part of Russia’s mobilization, as opposed to the battle-hardened contract soldiers and irregular forces fighting in Ukraine’s east and south.

Putting those conscripts at risk poses a political risk for President Vladimir V. Putin of Russia; in Ukraine, Mr. Zelensky has referred to an “exchange fund” that Ukraine has starkly increased.

Kyiv may be sending a message.

The real goals of the operation may not be on the Russia battlefield.

After the failure of Ukraine’s much-advertised counteroffensive last year and the ongoing losses in the east, it appears to be trying to change the war’s narrative.

The Ukrainians may be trying to convince the West that they will not give up, and that the United States in particular should allow them to use American long-range cruise missiles inside Russia.

After all, it has happened before: Over the 30 months of this war, the United States has repeatedly refused to supply Ukraine with certain kinds of weapons or to use those weapons in certain ways, only to then relent.

Over the past week, Mr. Zelensky has raised the issue of striking Russia with Western-supplied long-range missiles at least four times in his nightly video addresses.

“We need appropriate permissions from our partners to use long-range weapons,” he said on Monday. “This is something that can significantly advance the just end of this war.”

The announcement that a new version of mpox had been discovered in Sweden this week was the first indication that the disease had slipped out of Africa, where it has caused an escalating crisis in the Democratic Republic of Congo.

The announcement on Thursday about the disease formerly known as monkeypox came just a day after the World Health Organization declared a global health emergency, and it confirmed fears that a further spread was inevitable.

The person with the disease in Sweden had traveled to an area affected by the disease.

The European Center for Disease Prevention and Control said it was “highly likely” that more imported cases would be confirmed, in large part because of frequent travel between Europe and Africa. The center advised member countries to increase preparedness and to issue travel advisories recommending that people traveling to affected areas see if they are eligible for vaccination.

Pamela Rendi-Wagner, the E.C.D.C. director, warned that as long as the outbreak in Africa was not under control, cases would continue to appear in Europe and North America too.

“We have to be concerned, even outside Africa, because with the increasing number and the fast spread, the likelihood of the introduction of cases in Europe and the U.S. will increase,” Dr. Rendi-Wagner said in an interview on Friday.

The E.C.D.C. on Friday raised the risk of people in the European Union contracting the new version from “very low” to “low,” but emphasized that people traveling to and from the affected areas in Africa need to take precautions and are at a high risk.

What do we know about the case in Sweden?

The new version of the disease that is dominant in Congo is known as Clade I. The older version, a form of which caused a global outbreak in 2022, is known as Clade II. (A clade is a genetically and clinically distinct group of viruses.)

The Swedish patient was the first Clade I case diagnosed outside of Africa.

The person was quickly diagnosed, treated and isolated in the Stockholm area, while health workers began contact tracing, according to Magnus Gisslen, a state epidemiologist with the Public Health Agency of Sweden. While Dr. Gisslen said no new cases have been identified, fears of a wider transmission remain.

“People are afraid. There are flashbacks to the Covid-19 pandemic,” Dr. Gisslen said, adding that his office had fielded concerned calls from people who had planned to travel to the affected region.

Sweden, Italy and Britain have all issued public health warnings and preparedness strategies.

Is this outbreak different from the one in 2022?

The short answer is: Yes.

Dr. Paul Hunter, an epidemiologist at Norwich University in England, notes that “we’ve got two epidemics going on.”

The 2022 outbreak was driven by a version called Clade IIb, which is predominantly spread through sexual contact. Men who had sex with men proved to be the most at-risk population, but behavioral changes and vaccinations curbed the spread. New infections are still occurring, and the W.H.O. reported 100 new cases in Europe in June and 175 in the Americas.

The deadlier Clade I version has caused 15,600 infections and 537 deaths in the Democratic Republic of Congo, according to African health authorities.

Clade I is further differentiated by how it is transmitted, and who is most vulnerable. Clade Ia is spread through household contact and exposure to affected animals, in addition to sexual contact. So far, it is young children who are most vulnerable to this subtype. It is unclear if children on other continents will be as susceptible because it’s not yet certain how the children in Africa are contracting the disease.

So far, Clade Ib appears to spread mainly through heterosexual sex. Swedish doctors confirmed that the patient in Stockholm has this subtype.

Mpox may resemble ordinary respiratory illnesses at first but later manifests as a raised rash in the mouth, hands, feet or genitals. The virus spreads mainly through close contact — directly with the skin or fluids of an infected person, or with contaminated bed linens and other items.

Two doses of the mpox vaccine Jynneos, made by the Danish drugmaker Bavarian Nordic and used against the 2022 version, should protect against all versions of the virus, experts said.

As with many other infections, most people with healthy immune systems are unlikely to become severely ill with mpox.

Has this new version spread elsewhere?

So far, Sweden is the only country outside of Africa that has identified a case of the new version.

Pakistan announced a new case of mpox Thursday, but health workers were still trying to figure out which form of mpox the patient has. A senior health official in Peshawar said the infected person was a 34-year-old who had recently traveled from a Persian Gulf state and was the first case reported in the country since the beginning of the year.

For the moment, Dr. Giovanni Rezza, Italy’s former director general for prevention, and now a public health professor at San Raffaele University in Milan, considers the latest mpox outbreak a “regional emergency” in Africa, but says other places need to prepare now.

“It’s clear that Europe needs to keep its eyes open,” Dr. Rezza said.

What can Europe do to slow the spread of mpox?

Besides trying to stop the spread in Europe by raising awareness among health professionals, by treating patients promptly and by testing close contacts, European countries can also try to help stem the disease in Africa.

The European Union said on Wednesday that it would donate more than 175,000 doses of the mpox vaccine to countries in Africa, Bavarian Nordic will donate 40,000 doses that will be distributed by the Africa Centers for Disease Control and Prevention and the United States is donating 50,000 doses. France also said it would donate vaccine doses to the affected countries in Africa.

Reporting was contributed by Apoorva Mandavilli, Emma Bubola, Zia ur-Rehman Rachel Chaundler and Ségolène Le Stradic.