After Daria fled from her Russian-occupied village to western Ukraine, she spent weeks restlessly wandering the streets. Whenever she grew tired of walking, she would sit on park benches and tell anyone who would listen — even perfect strangers — what the Russian soldiers did to her.

“I wanted to tell everyone, but there was no one to talk to,” recalled Daria, a 32-year-old illustrator. “I could not confide in my family members, and I did not know anyone in town. I had to somehow deal with it on my own.”

Daria said Russian soldiers raped her twice in March 2022 in Havronshchyna — a small village about 30 miles from Kyiv, Ukraine’s capital — where a range of alleged war crimes, including sexual violence, have been documented by Ukrainian authorities and international media.

For two years after the assault, Daria said, she wrestled with shame. She could not tell her father what happened, and she struggled to be intimate with her partner. She said in an interview that she was ready to tell her story, to erase the stigma of sexual assault and help herself and other victims heal.

Her plight resonates with many other Ukrainians. Behind the battlefields of Europe’s largest war in 80 years, the authorities and aid groups say, there are thousands of women, men and children who have been sexually assaulted by Russian soldiers and have been struggling to piece their lives back together.

Ukraine’s government, despite facing one of the toughest moments since the beginning of the full-scale invasion in February 2022 with almost nonexistent battlefield progress, has made significant efforts to document and prosecute sexual violence cases.

But victims and advocates say that it has failed to put in place an adequate support system for survivors, leaving them largely on their own to deal with the financial and psychological effects of their trauma.

Some women said they had to pay for medical checkups or psychotherapy sessions from their own pockets. Many who were dealing with insomnia and panic attacks relied not on the government for help, but on charities, which organize group therapy sessions and connect women with volunteer therapists.

Sexual violence is a war crime under international law, but not under Ukrainian law. Because of that, many victims have not received the same legal status and financial support as victims of other war crimes. Parliament is currently considering a law that would create a legal definition of sexual violence while also establishing measures to provide free therapy for victims and rapid financial help for those in urgent need.

Despite evidence gathered by the United Nations suggesting that sexual violence by Russian forces in Ukraine has been widespread, it remains a mostly hidden casualty of the war. Of almost 137,000 reports of war crimes investigated by Ukraine’s prosecutor’s office, only 308 involve sexual violence.

Experts on sexual violence during conflict said that this was a significant number considering the challenges of operating during a war, and the authorities attributed the low percentage to the reluctance of most victims to report such crimes.

Anna Sosonska, the head of the division for conflict-related sexual violence in Ukraine’s prosecutor’s office, said the majority of victims do not want to relive their traumatizing experience, or risk the stigmatization that might come with speaking publicly. Many survivors live in territories occupied by the Russian Army, she said, further complicating attempts to prosecute.

“Rape is the most underreported and dismissed crime,” said Wiola Rębecka-Davie, a New York-based therapist specializing in conflict-related sexual violence. “Even more in the time of war, when carrying out statistics on sexual violence is never a priority.”

While atrocities since the invasion have received international media scrutiny, sexual assault by Russian forces has been a concern in Ukraine since Russian proxy forces poured into eastern Ukraine in 2014, igniting eight years of simmering hostilities and the occupation of parts of Ukrainian territory. Some victims are coming forward only now after dealing with shame and fears of stigmatization.

The New York Times interviewed almost two dozen women, sexual violence experts, psychologists and activists for this article. Seven survivors of sexual assault, aged 32 to 62, including a safety engineer and a theater director, provided accounts of their experiences. The earliest case involved a 56-year-old anesthesiologist, who said Russian troops sexually abused her in October 2017 in Donetsk. The most recent involved a 48-year-old civil servant, who said she was assaulted in August 2022 in Kherson.

The women agreed to speak using only their first names to maintain privacy involving a sensitive topic; several agreed to be shown in photographs. Their accounts have largely been corroborated by the prosecutor general’s office and SEMA, the global network for survivors of conflict-related sexual violence.

The crimes being investigated by Ukraine’s prosecutor’s office include rape, attempted rape, mutilation of genitals and forced nudity, among others. Some people were forced to watch the sexual abuse of loved ones. The cases concern people from 4 to 82 years old from a big swath of Ukraine’s territory, including the regions of Kyiv, Kherson, Donetsk and Zaporizhzhia.

When asked for comment, the press office of the Kremlin said, “Most often claims of Ukrainian representatives are groundless.”

Halyna, 61, a pensioner from Dmytrivka, said she was assaulted by a Russian soldier in his twenties.

“First, he raped me with his fingers,” Halyna said. “Then with the rifle. He laughed and laughed and laughed throughout the whole thing. Whenever I cried, he told me to shut up or else he would kill me.”

When he was finished, Halyna said, she was bleeding.

For over a year, she said, she could not sleep. Whenever she closed her eyes, she saw Russian soldiers climbing her fence. Despite that, she still lives in the home where the assault happened.

“Where else should I go?” she said. “My pension comes down to 2,700 hryvnia,” or about $66, a month.

Experts say Ukraine has had an impressive track record when it comes to advancing investigations to actual criminal proceedings, despite the difficulty of prosecuting soldiers from an opposing army. As of this month, Ukrainian investigators have sent 30 indictments of Russian soldiers to the court; five have been convicted in absentia.

But experts said that by focusing primarily on the legal process, the state has neglected the material and psychological needs of the survivors.

“Legal avenues take a lot of time, and they are expensive,” said Emily Prey from the New Lines Institute for Strategy and Policy, a Washington D.C.-based research institution. “What’s needed is interim reparations, access to free health care and access to free housing.”

Kateryna Pavlichenko, Ukraine’s deputy interior minister, said that documenting sexual crimes has become a priority for the government. The authorities trained special police units to work with survivors, she said, and set up nine support centers across the country offering psychological and medical help.

She said that over the past few years, the government had developed new investigation methods, putting priority on the protection of victims and witnesses, including their safety, privacy and dignity.

Some women who gathered the courage to speak to the authorities said that instead of getting help, they found more humiliation.

Halyna, the pensioner, said that as soon as the first Ukrainian soldiers arrived in her village, she started asking them to take her to a hospital. She was suffering from a high fever that she believed was caused by infected wounds from the rape. But it was not until nearly a month later that she was taken to Kyiv to see a doctor and two investigators from the prosecutor’s office.

“Take off your clothes and lie down on the chair,” one of the investigators instructed her, Halyna said, recounting the episode. “The doctor won’t be looking at you, I will.”

She said she had to beg the gynecologist to be properly examined and tested for H.I.V. and venereal diseases, and she paid for it from her own pocket. There were no witnesses in the room, but several months later she recounted the episode to SEMA, the survivor’s network.

Despite her frustration, she said she can understand why she was treated this way. “The full-blown war had just begun,” she said. “There were no services in place, no one was prepared.” She said she believed support for survivors had improved since then.

Daria, the illustrator, said that after she reached relative safety, she went to a few psychotherapy sessions, which she paid for herself, but that they did not help. So she just kept walking.

After about six months, something shifted. She was determined to move on from surviving to living.

She picked up new hobbies. She finally confided in her mother and her boyfriend — and this past spring, she told her father what happened to her.

One day, during a train commute, Daria felt a sudden need to draw. Back home, she sketched two pairs of eyes — hers and her father’s — lurking through gaps in the attic wall, and watching Russian soldiers enter Havronshchyna in March 2022.

Over the following months, she drew scenes of the occupation and of the assault on her. Representing her trauma on paper empowered her to finally report her case to the authorities.

She also decided to confront her shame head-on, and displayed some of the deeply personal sketches at an exhibition in Kyiv this past spring.

“This is my personal reflection and self-therapy,” she said of the exhibition. But she hoped that it would alleviate the stigma and help others deal with their trauma.

“It is important to testify about crimes,” she said, or else “other people will speak for us.”

A rocket from Lebanon struck a soccer field on Saturday in the Israeli-controlled Golan Heights, killing at least 12 people, mostly teenagers and children, according to the Israeli military. It was the deadliest single attack from across Israel’s northern border in months of hostilities and raised fears of an escalation in the conflict.

Israeli officials accused Hezbollah, the politically powerful Lebanese armed group, of firing the rocket and vowed to respond. Hezbollah denied responsibility, although the group did say it had launched several barrages of missiles at northern Israel on Saturday.

The Israeli emergency rescue service, Magen David Adom, said that in addition to the 12 dead, about 20 people had been wounded, some of them seriously, in the Druse town of Majdal Shams. The Israeli military said that the ages of those killed or wounded ranged from 10 to 20 years old, and that they had been playing soccer at the time of the attack.

Idan Avshalom, a paramedic with Magen David Adom, described a “gruesome” scene at the soccer field, with bodies on the ground and fires burning. “We immediately began triage,” he said.

Even as Israel has waged a nearly 10-month-long war with Hamas in Gaza to the south, it has traded fire with Hezbollah to the north; both groups are backed by Iran, Israel’s regional adversary. Hezbollah began shooting missiles and drones at Israel shortly after Hamas launched its Oct. 7 attack that set off the war in Gaza.

For months, the well-armed Hezbollah has fired thousands of missiles and drones at Israel in solidarity with Hamas, leading tens of thousands of Israelis to evacuate their homes. Israel has retaliated in Lebanon, devastating towns near the border, prompting more than 90,000 to flee north and killing more than 460 people, mostly militants.

At the same time, the two sides have sought to avoid igniting a full-blown war, which would likely devastate both Israel and Lebanon. But experts have warned that a deadly miscalculation could ignite a broader escalation, and on both sides of the border, Israelis and Lebanese were left wondering on Saturday night whether the attack on Majdal Shams was just that.

The attack caught Prime Minister Benjamin Netanyahu of Israel in the United States, where he has spent the last few days meeting with President Biden and Donald J. Trump, who is running for president again. Mr. Netanyahu’s office said he had instructed that his return flight be made as early as possible.

“Israel will not overlook this murderous attack,” Mr. Netanyahu said in a statement distributed by his office. “Hezbollah will pay a heavy price which it has not paid up to now.”

Rear Adm. Daniel Hagari, the Israeli military spokesman, told reporters that the rocket that struck the soccer field was an Iranian model — a Falaq-1 — that carried a 50-kilogram warhead. He said that only Hezbollah possessed those rockets in Lebanon.

“We will act to restore full security on our northern border,” Admiral Hagari said.

Israel seized the Golan Heights from Syria during the 1967 war, and it is home to more than 20,000 Druse Arabs. Israel effectively annexed the territory in 1981, a move that was widely rejected by the international community. Nearly four decades later, President Donald J. Trump signed a proclamation recognizing Israeli sovereignty over the plateau, but other powerful countries have not followed suit.

There are four Druse villages in the Golan; their Arabic-speaking residents practice a largely esoteric religion that is often described as an offshoot of Ismaili Islam. While many residents feel loyal to Syria, thousands have become Israeli citizens.

Residents of the town of Majdal Shams expressed horror and sadness in the wake of the deadly strike.

“I didn’t expect that our village would be hit, but it’s happened now,” said Madad al-Shaer, 50, an owner of a falafel and hummus restaurant. “No one is protected. It doesn’t matter if you’re living in a Druse or Jewish village.”

Mr. Shaer, a father of three, said that his daughter frequently played at the soccer field that was struck, but that she was not there on Saturday.

In a Facebook post, the Majdal Shams local council said that “a dark day” had befallen the village and called on people to stay in their homes.

The Biden administration has sought to mediate a truce between Israel and Hezbollah, including by dispatching Amos Hochstein, a senior adviser to the president, to meet with senior officials in Jerusalem and Beirut.

“The United States will continue to support efforts to end these terrible attacks along the Blue Line, which must be a top priority,” the White House’s National Security Council said in a statement on Saturday, referring to the demarcation between Israel, Lebanon and the Golan Heights. “Our support for Israel’s security is ironclad.”

But Hezbollah has said it will not cease its attacks until Israel ends its campaign in Gaza — a prospect that remains remote.

The strike on Majdal Shams was likely to increase the pressure on Mr. Netanyahu’s government to respond more forcefully to Hezbollah’s rocket and drone attacks, which have escalated in recent weeks.

Nearly 10 months into the war, the roughly 60,000 Israelis evacuated from communities near the border remain displaced. They have little idea of when they might return, and some say only a major operation against Hezbollah will make them feel safe enough to go back home.

Right-wing Israeli lawmakers called for Israel to launch a major military operation against Hezbollah in response to the strike. Bezalel Smotrich, a far-right government minister, has argued for months that Israel should create a buffer zone inside Lebanon to drive Hezbollah away from the border.

“For the death of small children, Nasrallah should pay with his head.” Mr. Smotrich wrote on social media after the attack on Saturday, referring to Hassan Nasrallah, the secretary-general of Hezbollah. “Lebanon as a whole has to pay the price.”

Mohanad Hage Ali, a Beirut-based fellow at the Carnegie Middle East Center, said that there would be a “strong Israeli response” to the strike, but that Hezbollah would in turn demonstrate restraint so as not to risk all-out war.

Without naming Hezbollah or any other militant group, the Lebanese government condemned “all acts of violence and aggression” against all civilians and called targeting them “a flagrant violation of international law.”

Israel and Hezbollah last fought a major land war in 2006, after the Lebanese militants abducted and killed Israeli soldiers in a cross-border ambush. Large swaths of Beirut were devastated in the battle; Mr. Nasrallah later conceded that he would not have launched the attack if he had foreseen its deadly consequences.

More than 1,000 Lebanese and 150 Israelis were killed in the 2006 war. During that conflict, a rocket fired by Hezbollah killed two Arab children in the city of Nazareth in Israel. Mr. Nasrallah later made a public apology.

Euan Ward contributed reporting from Beirut, Lebanon, and Peter Baker from Washington.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The Israeli army ordered the evacuation of several neighborhoods in southern Gaza on Saturday, the latest in a series of such directives recently that have forced tens of thousands of displaced Palestinians to relocate yet again.

The decision affects an area around the city of Khan Younis that Israel had previously designated a “humanitarian zone” for Palestinian civilians, who are weary from nearly a year of unrelenting war and a daily struggle to avoid disease and find enough food and clean water to survive.

“People aren’t being regarded as people,” said Juliette Touma, a spokeswoman for UNRWA, the main United Nations agency providing aid to Palestinians in Gaza. “They’re being treated as pinballs and chess pieces.”

The Israeli military said its recent evacuations and operations in Khan Younis have targeted a renewed Hamas insurgency and accused Hamas of installing weapons infrastructure in the area under the latest evacuation order on Saturday.

Over the past week, amid new evacuation orders, more than 190,000 people have fled the places where they were sheltering in southern and central Gaza, the United Nations said on Friday.

Dozens of people have been killed in fighting in the area, according to both Israel and Palestinian health officials. The Israeli military said on Friday that its forces had killed more than 100 militants in Khan Younis in recent days, while Palestinian health officials have said that at least some casualties arriving at local hospitals with severe blast wounds have been women and children.

There was also a new Israeli strike in central Gaza on Saturday, in an area some miles north of the zone under the latest evacuation order. Palestinian health officials reported that the Israeli military struck a school-turned-shelter that the Al-Aqsa hospital in the town of Deir al-Balah was using to provide medical services to Palestinians.

More than 30 people were killed in the Israeli attack and scores more wounded, according to Khalil al-Daqran, a spokesman for the Al-Aqsa hospital.

The Israeli military said its forces had struck a Hamas command and control center within the school grounds, which it claimed had been used to wage attacks against the Israeli military and store weapons.

Tariq Abutaha, 30, said in an interview on Saturday that he had fled his home in the Khan Younis suburb of Qizan al-Najjar — inside the zone under the new evacuation order — on Friday as rumors of an impending Israeli operation swirled. He last left there in December, expecting to return a week or two later. But he returned after five months of fighting in the city to find his home partially ruined.

On Friday evening, Mr. Abutaha said he paid $400 for a small truck to ferry 20 family members and whatever belongings they could load to the coastal area of Al Mawasi, which Israel has called a “safer zone” since the early days of the war. As they drove, he watched one scene after another of people fleeing on foot or camping out amid the rubble in the streets.

“We want to get back to our lives. By God, we’re exhausted,” said Mr. Abutaha, as he settled in, once again, in a crowded tent on Gaza’s coast.

Hassan Shehada, 61, a displaced person in Qizan al-Najjar, said he and 25 family members had failed to find a place to go and would remain in the evacuation area, at least until Sunday morning, despite Israel’s orders.

“We have no idea what to do. This is a real problem. We’re tired of moving over and over,” he said, likening life in Gaza to going through “a slow death.”

In any case, fleeing to comply with Israeli evacuation orders provides little guarantee of safety for Palestinian civilians.

The Israeli military has said it will target Hamas anywhere the armed group operates, contending it has used schools, hospitals, and the Israeli-designated “safer zone” for military purposes.

Israeli ground forces invaded Khan Younis in December, beginning a four-month battle that devastated the city. After the troops withdrew in April, some residents returned to their homes, began clearing streets, and sought to rebuild their lives as much as possible.

Then came another wave of Israeli evacuation orders in early July, followed by at least two more sets of instructions for Palestinians to flee their neighborhoods. For many, it was far from their first time fleeing their homes.

Kamal al-Madhoun, 66, said he saw hundreds of displaced people arriving in western Khan Younis on Saturday, carrying heavy bags and looks of desperation on their faces.

Watching the people trying to find a place to set up makeshift shelters worried Mr. al-Madhoun, who wondered whether he might find himself in the same situation next.

“Absolutely nothing is permanent,” he said. “We’re always full of fear that we’ll have to go through that miserable experience again.”

The Israeli military said another reason for the wide-scale operations in this area recently was an attempt to recover the bodies of Israeli hostages.

Israeli forces worked for almost 30 hours on Wednesday to extract the bodies of five hostages from a tunnel shaft nearly 200 meters long and 20 meters underground, the military said.

“We were right next to those bodies in the past” without knowing it, lamented Lt. Gen. Herzi Halevi, the Israeli military chief of staff. “We didn’t know how to reach them.”

The operation in Khan Younis was escalating again just days after Prime Minister Benjamin Netanyahu of Israel met with President Biden in Washington, where they discussed efforts to reach a cease-fire in Gaza that would also free the roughly 115 living and dead hostages there.

The negotiations appear to have ground to a halt in recent weeks, despite some renewed optimism. Israel has yet to formally issue its response to Hamas’s latest counterproposal, which the Palestinian group handed to Qatari and Egyptian mediators in early July.

Relatives of several American-Israeli hostages met with Mr. Biden and Mr. Netanyahu on Thursday. After the discussions, they expressed hope that an agreement could yet go forward; in November, roughly 105 of the 250 hostages were freed in a weeklong truce.

“We feel probably more optimistic than we have since the first round of releases in late November,” Jonathan Dekel-Chen, whose son Sagui was abducted during the Hamas-led Oct. 7 attack, told reporters at a news conference.

Ronen Bergman contributed reporting to this article.

In the dark early morning, they cut into a fence protecting the high-speed rail line right outside the small town of Croisilles. Once past the fence, the culprits soldered open the metal protective cover of a culvert alongside the tracks. Then, they poured flammable liquid and set a fire, damaging around 40 cables, explained the local mayor, Gérard Dué.

Arsonists did not just strike there, 105 miles north of Paris. Around the same time, at 4 a.m., they struck cables along high-speed rail lines at one site east of the capital and another to the west.

In all three cases, their targets were precise: They chose signaling stations close to where the tracks split in two directions.

“We were in the dark on three of our principal lines in our rail network,” said Christophe Fanichet, the president of the national railway company’s passenger trains division, S.N.C.F Voyageurs.

Toiling in the rain, and often in the dark, rail workers managed the delicate task of repairing fiber optic cables. By Saturday morning, all trains rushing from Paris to the east were back on schedule, and seven of 10 trains heading north, west and southwest were running, albeit not at their full speed, which can reach 320 kilometers, or 186 miles, an hour.

While claiming success in the face of terrible stress on the day of the opening ceremony of the Olympics in Paris, the question facing rail workers still remains: Who did this and why?

“These people knew what to look for,” said Axel Persson, a train driver and union leader on slower rails with S.N.C.F. “They hit specific cables that pass information for traffic controllers and traffic supervisors to know what’s happening on the high-speed lines. They seem to have been quite precise in their work.”

French authorities suspect a fourth attack was in the making — this one southeast of Paris. But it was foiled by maintenance workers with the railway who came upon suspicious individuals, sending them fleeing before any damage was done, the authorities said.

They have so far said little about the suspects or their motives. No one has publicly claimed responsibility for the attacks. The Paris prosecutor’s office, which handles major cases of organized crime, has put some 50 investigators on the case, two ministers said.

Unsettling under normal circumstances, the coordinated attack came at a critical time: on the morning of the unorthodox open-air opening ceremony, when hundreds of thousands of visitors were scheduled to pour into Paris and many Parisians were fleeing the city for their summer vacations.

Since the attack, the authorities have deployed about 1,000 railway workers, 250 railway security agents, 50 drones and several police helicopters to monitor France’s vast railway network, where traffic is expected to return to normal on Monday.

“The goal is to avoid a new sabotage operation,” Patrice Vergriete, France’s transportation minister, told reporters in Paris on Saturday. “We are on alert.”

Sources close to France’s intelligence agency said the attacks had some of the hallmarks of far-left anarchist groups. But France has also been put on high alert for foreign interference, particularly by Russian actors.

This past week, the police arrested and charged a 40-year-old Russian man in Paris with working at the behest of a foreign power to “provoke hostilities” in France, intending to destabilize the Olympic Games.

About 35 million euros a year, or about $38 million, is spent to protect the country’s vast and bustling train network, said Jean-Pierre Farandou, the national railway company’s president. The prized high-speed network gets special protection, with fencing and drones carrying thermal cameras, he said.

But, stretching 3,100 miles, “you can’t put a camera or a police officer at every kilometer,” he said.

The entirety of the network covers about 18,000 miles of tracks used by 15,000 trains every day.

Mr. Vergriete acknowledged that the authorities had focused on the Paris region leading up to the Olympics, reinforcing security there with an extra €5 million, but not elsewhere in the country.

“We had no particular prior warning about any danger for the network’s security,” Mr. Vergriete said. “Surveillance of the network was normal.”

“Now that we are on alert,” he added, “we are going to use much more consequential means.”

By focusing on the very centralized signaling system, and not the rails or overhead electric cables, the arsonists attacked the nerve center of the rail system, said François Delétraz, the president a federation of groups representing transportation passengers.

“A lot of intelligence went into this,” Mr. Delétraz said. “It’s like attacking a colossus at its weak spot.”

Video released on Friday by the S.N.C.F. showed workers clad in fluorescent orange hunched over clumps of charred cables as they painstakingly replaced them.

Each cable is split into dozens or even hundreds of fiber optic threads that must be repaired, reconnected and tested.

Their fast work softened the effect of disruptions that threatened to complicate the trips of more than one million travelers on Friday and over the weekend. Instead, only 100,000 people had trains canceled on Friday, and only 20 percent of the weekend’s 800,000 travelers had their trips canceled. Mr. Farandou said all Olympic teams booked on trains on Friday had arrived.

“Today, my predominant feeling is a form of pride,” Mr. Farandou said. “I am proud of these railway workers.”

Sabotage on rail lines is not uncommon in France.

In January 2023, someone pried open and set fire to electric cable boxes at a signal station in Vaires-sur-Marne, about 10 miles east of Paris, blocking traffic on the eastern high-speed line for several days. An investigation was opened that month — a time when protests against President Emmanuel Macron’s decision to raise the legal retirement age were in full swing.

But the case was later dropped because the perpetrators were never identified, according to the prosecutor’s office in Meaux, which handled the case.

Then, in April 2023, arson damaged signaling infrastructure in the Landes, in southwestern France, disrupting train traffic in that region. The transportation minister at the time vowed that “this outrageous act will be punished.” Local prosecutors did not immediately respond to a request for comment on whether any arrests were made in that case, but none appear to have been publicly reported.

Perhaps the most famous case of train tampering involved the Tarnac Nine — a group of young people arrested in 2008 and accused of draping horseshoe-shaped iron bars over 25,000-volt power lines to disable trains. The police and prosecutors said they were dangerous anarchists bent on overthrowing the state.

But when the case finally came to trial in 2018, French judges acquitted almost all of them on the sabotage charges.

In the case of Friday’s coordinated attacks, the potential charges include criminal conspiracy, “damage to property likely to affect the fundamental interests of the nation” and “damage and attempted damage by dangerous means in an organized gang.” They carry the risk of up to 20 years in prison and hundreds of thousands of euros in fines.