Israeli leaders have long insisted that they will not end the war until Hamas is destroyed. That appeared far from reality on Sunday as Hamas militants, some waving rifles, fanned out in parts of Gaza in pickup trucks, in a show of authority to Palestinians and Israelis alike.

Israel and Hamas have both preserved some of their bargaining chips. At the end of the 42-day truce, Hamas will still have around two-thirds of the 98 remaining hostages, including dozens who are believed to be dead. And Israel will still occupy parts of Gaza, and hold major prisoners, including Marwan Barghouti, a militant leader and iconic Palestinian political figure.

But as part of the talks, the Israeli government will then likely have to choose whether it is willing to choose one of its war aims, bringing home the hostages, over another, destroying Hamas. And choosing the hostages might threaten Prime Minister Benjamin Netanyahu’s grip on power in Israel.

In the meantime, both sides have agreed to postpone a decisive agreement as to the war’s end and the future of Gaza, and hope the 42-day cease-fire will play to their advantage, said Shlomo Brom, a retired Israeli brigadier general. Hamas, in particular, “hopes that the new dynamic will prevent Israel from returning to fighting,” he said.

The decision to accept a temporary cease-fire opened deep fissures within Mr. Netanyahu’s governing coalition, which is stacked with hard-liners. Itamar Ben-Gvir, the far-right national security minister, resigned in protest from the cabinet and withdrew his Jewish Power party from the coalition on Sunday.

The Religious Zionism party, led by Bezalel Smotrich, threatened to bolt the coalition, too, if Mr. Netanyahu failed to renew the fighting after the end of the 42-day truce. If Mr. Smotrich’s party also left, Mr. Netanyahu’s government would hold fewer than half of the seats in the Knesset, Israel’s Parliament, which could cause the government to fall and force new elections.

On Saturday night, Mr. Netanyahu stressed that the cease-fire was temporary for now. He argued that Israel retained the right to return to the war if “the second stage negotiations are ineffectual,” adding that President-elect Donald J. Trump would support Israel’s decision.

“We retain the right to return to the war, if necessary, with the backing of the United States,” Mr. Netanyahu said in a televised address.

The truce’s fragility was underscored on Sunday morning when Hamas did not immediately hand over a list of hostages to be released to Israel, prompting a nearly three-hour delay in the cease-fire. Analysts say the deal will likely see numerous similar tests over the next few weeks as both sides flex their muscles.

The families of Israeli hostages still held in Gaza have called on the Israeli government to bring home the remaining captives by fulfilling all the phases of the deal. Noa Argamani, a freed hostage whose boyfriend, Avinatan Or, remains in captivity, said that it broke her heart that he was not going to be freed in this round.

“The progress in the past few days is a very important step, but the deal must go through in full, completely, in all of its stages,” Ms. Argamani said in a speech in Miami on Thursday.

Riyadh al-Gharably, 64, said he had hardly slept as he and his family waited to see if the cease-fire would go into effect as planned. He spent Sunday morning watching a clock and listening to sporadic artillery shelling and gunfire echoing from the city’s eastern borders — hoping that they did not signal any scuttling of the long-awaited peace.

“All the wives here cried all night,” said Mr. al-Gharably, his voice breaking.

In Gaza City, members of Palestinian Civil Defense teams — who carried out rescue operations in response to near-daily Israeli strikes during the war — poured into the streets to celebrate and climbed on top of ambulances to wave Palestinian flags.

In Deir al Balah, a city in central Gaza, cars honked their horns and loud music blared from coffee shops.

For many, the moment was awash with conflicting emotions: There was the sheer joy that the bombing and bloodshed might finally — finally — be over. But there was also an overwhelming sense of loss resulting from a conflict that has devastated the territory and its population.

Many people said they were determined to start to reclaim the lives they had once known despite the huge amount of destruction across the enclave.

“The joy of returning home is overwhelming, but it’s mixed with sadness,” said Ahed al-Okka, 52.

A construction worker from Gaza City in the north, Mr. al-Okka said that he has spent most of the past year living in a tent on the streets of a city in central Gaza, Deir al-Balah. He planned to return Sunday to his house, which he had heard was partially damaged but still standing.

But even if his family could repair a single room and live in it, that would be enough for now, he said: “We’ll rebuild and fix things step by step and finally get some peace of mind.”

For others, the resolve to rebuild lives disrupted by war was overshadowed by the grief and pain built up over 15 months of conflict.

“I can’t say I’m happy about this truce,” said Suhaila Dawaas, a 55-year-old mother of eight who was displaced to central Gaza from Beit Lahia in the north. “What is left for us after everything — after the endless losses, the destruction, the pain?”

Ms. Dawaas said several of her relatives had been killed by Israeli airstrikes. Her home has been mostly destroyed, she said, and she hoped to find a few reminders of the life her family once had in the rubble — maybe in photo albums — when she returns home.

She said she was grieving for more than what had been lost. She added that she was also grieving for everything still to be lost — her children’s future and the hardships that would undoubtedly define the next chapter in Gaza as people try to rebuild their lives.

“We spent our entire lives building homes for our children, and now, we have lost so much,” Ms. Dawaas said. But, “I am grateful that the survivors will now have a chance at some peace.”

“The rock lying on my heart has been removed,” said Dov Weissglas, a former Israeli politician. “We want to see the hostages home, period.”

But — both men also had a “but” — Mr. Obeid has not seen his damaged house in northern Gaza for more than a year. How bad, he wondered, is the damage? And who will rebuild a decimated Gaza?

Mr. Weissglas worried about the condition of the hostages set to be freed gradually over the next few weeks from dank quarters in the territory. And he grimaced about exchanging them for hundreds of Palestinian detainees, many of whom are serving life sentences for attacks on Israelis. “There is relief,” he said, “wrapped in caution, fears and concern.”

It was an apt summary of the mood on both sides of the Israeli-Palestinian divide on Sunday, as Israelis and Palestinians expressed feelings of elation tinged with doubt.

For Palestinians, the truce is theoretically expected to provide at least six weeks without strikes on Gaza. That offers a window for Gazans to take tentative first steps toward reconstruction; to find relatives still buried in the rubble; and to come to terms with the killing of more than 45,000 people, both civilians and combatants, whose bodies have already been counted by the Gazan health authorities.

For Israelis, the deal allows for the gradual release of at least 33 of the hostages captured during Hamas’s raid on Israel on Oct. 7, 2023 — an attack that killed up to 1,200 people and provoked Israel’s devastating 15-month response. For the hostages released alive, that means freedom after 470 days of captivity. For Israelis at large, many of them wracked by a form of survivors’ guilt, it offers qualified catharsis.

But the details of the deal between Israel and Hamas mean that both sides still face considerable uncertainty about how the next six weeks will play out, let alone about whether the tentative arrangement will later become permanent. Even the first phase started hours behind schedule on Sunday morning, amid disputes about which hostages would be released in the afternoon. In that time, according to the Gazan authorities, Israeli strikes killed and wounded yet more people.

Palestinians remain unclear about the fates of several thousand Gazans detained incommunicado during the war and who may not be released during the upcoming exchanges. Reema Diab, a housewife in central Gaza, still has no way of locating her husband, a horse trainer, who she said was taken for interrogation in Israel in December 2023 and never heard from since.

“I’m relieved the bloodshed is coming to an end, but my heart aches,” Ms. Diab said. “His absence is unimaginable.”

A few dozen miles away, Mr. Weissglas feared for the fates of some 65 hostages who may not be released from Gaza if the deal collapses after six weeks. He worried that many of the initial 33 hostages set to be released over the next 42 days may be emotionally or physically scarred, or even dead. And he lamented the cost of their freedom, which will be obtained in exchange for Palestinian detainees, including those convicted of major terrorist attacks as well as teenagers who have never been charged.

Palestinians see the soon-to-be released prisoners as freedom fighters. For Israelis, it will be a psychological blow to see “this stream of murderers being released,” Mr. Weissglas said.

Videos of Hamas fighters re-emerging in triumph from hiding was also a gut-punch for Israelis, who had hoped the war would completely destroy the group’s military abilities. For many Gazans, it was a sight to be celebrated, but for others, it was a reminder of lingering uncertainty about Gaza’s future governance.

Mr. Obeid works for the Palestinian Authority, which lost power to Hamas in Gaza 18 years ago but which still employs some civil servants there, including Mr. Obeid. He said he had been working with the authority’s leaders in the West Bank to plan potential cleanup and reconstruction operations in Gaza in the coming days. It is unclear, he said, whether that will be possible with Hamas still in charge over the next six weeks.

But that is tomorrow’s challenge, Mr. Obeid said.

For now, he said, “I can breathe oxygen again.”

Bilal Shbair contributed reporting from Deir al Balah, Gaza Strip, and Aaron Boxerman from Jerusalem.

Here is what we know about the three hostages released on Sunday:

Romi Gonen

Ms. Gonen, was 23 when she was captured as she was trying to leave the Nova music festival in southern Israel when Hamas attacked. She was speaking at the time to her mother, Meirav Gonen, who she said had been shot and was bleeding.

Last February, Meirav Gonen released a recording of her last phone call with her daughter. She told Israeli news media that Romi was a strong and happy person who often went to raves.

In the early weeks of the war, her mother expressed concern that Israeli military operations in Gaza could endanger the hostages.

Romi Gonen’s older sister, Yarden, told The New York Times in February that she regularly went to a plaza in Tel Aviv where families of hostages have held vigils.

“None of us is doing anything remotely related to our previous lives,” she said.

Emily Damari

Ms. Damari, 27 at the time she was captured, is the only hostage with British citizenship still being held in January. She was taken from her home in Kibbutz Kfar Azza in southern Israel and was seen by a neighbor in her own car, driven by a militant, heading toward Gaza.

Ms. Damari was raised in Israel but traveled to Britain often, according to her mother, British-born Mandy Damari, who was in Israel in December to speak with officials and the news media and to plead for a hostage and cease-fire deal. She said her daughter had been shot and that she feared for her life, telling the BBC that she had welcomed the threats from President-elect Donald J. Trump that there would be “all hell to pay” if no deal was reached by his inauguration.

Last January, a hostage who had been released from Gaza, Dafna Elyakim, told Israeli news media that she and her younger sister had been taken into Hamas’s underground tunnels, where they met other female hostages including Ms. Damari.

On the eve of the first anniversary of the Oct. 7 attacks, Mandy Damari spoke at an event in Hyde Park in London, where she described her daughter as a soccer fan who enjoyed a drink and had “the classic British sense of humor, with a dash of Israeli chutzpah thrown in for good measure.”

Doron Steinbrecher

Ms. Steinbrecher, who was 30 when she was captured from her home in Kibbutz Kfar Azza, is a veterinary nurse with Romanian and Israeli citizenship. According to Israeli news media, she was in touch with her family on the kibbutz when the militants attacked, telling her parents that they had smashed her windows and shot into her room.

“They’ve arrived, they have me,” she said in a subsequent voice message sent to friends.

Last January, Hamas released a video clip of Ms. Steinbrecher and two other captives, Daniella Gilboa and Karina Ariev, in which they pleaded for their release.

Last March, on her 31st birthday, the Jewish News Syndicate published an interview with her mother, Simona Steinbrecher, who said that she had looked pale and thin in the video. She said she was concerned that Ms. Steinbrecher was not getting the daily medication she needed, though she did not specify what that was.

“She’s a strong woman, but it’s terrible being there,” Simona Steinbrecher said.

Hamas said the delay was because of technical reasons, but Prime Minister Benjamin Netanyahu’s office instructed the Israeli military not to proceed with preparations for starting the cease-fire until the names had been received.

The Israeli military also warned people in Gaza not to approach parts of the enclave where Israeli troops remained stationed.

While the delay unfolded, Israel’s strikes on Gaza continued. Rear Adm. Daniel Hagari, the chief spokesman for the Israeli military, delivered a televised statement at 8:30 a.m., saying the military would continue attacking in Gaza as long as the cease-fire had not come into effect. A spokesman for the Israeli military, speaking on condition of anonymity, confirmed that it had struck targets in Gaza after the proposed start time for the truce.

Mahmoud Basal, a spokesman for the Palestinian Civil Defense, an emergency service organization in Gaza, said in a statement around an hour later that Israeli bombardments were still occurring in several areas. He would eventually say that Israeli attacks had killed at least 19 people and injured more than three dozen others across Gaza during the delay, a figure that could not be independently verified.

At Al-Aqsa Hospital in central Gaza, people heard the sounds of Israeli drones, strikes and artillery shelling, said Ghada al-Kurd, 37. “The situation is still dangerous,” she said in a voice message.

Then, at about 10:30 a.m. local time, Hamas announced the names of the three Israeli hostages it would release on Sunday. Mr. Netanyahu’s office soon confirmed that information and said the cease-fire would come into effect at 11:15 a.m. local time — nearly three hours later than planned.