The Israeli military said on Monday that it had redeployed in areas of southern Lebanon, and repeated calls for Lebanese residents to wait for their approval before returning home. The Lebanese military had sent reinforcements to parts of southern Lebanon earlier in the day, preparing to enter some towns and safeguard civilians, Lebanon’s state-run news agency reported.

Israeli forces killed at least 24 people and injured over 134 others on Sunday, Lebanese officials said, after thousands of Lebanese marched to southern towns and villages. Those areas remain occupied by Israel past a 60-day deadline for its withdrawal under the November cease-fire agreement, which called for both Israel and Hezbollah forces to leave southern Lebanon and for the Lebanese Army and U.N. peacekeepers to deploy in force there.

The Israeli military said in a statement on Sunday that it had fired “warning shots” to disperse what it called “rioters.” Last week, Israel had indicated that it would remain in southern Lebanon despite the deadline, amid doubts about the Lebanese Army’s ability to stymie Hezbollah’s resurgence.

Negotiators had hoped that the U.S.-brokered cease-fire by now would have given way for a more permanent settlement. But as the 60-day deadline elapsed on Sunday, the White House issued a statement stating that the initial agreement would be extended until Feb. 18. The Lebanese prime minister’s office confirmed the extension, which they said followed discussions with U.S. officials. The flurry of diplomatic activity appeared designed to buy time and stave off further bouts of violence.

The bloodshed on Sunday sparked urgent calls for restraint by the U.N. amid growing fears of a sustained Israeli occupation and renewed hostilities between Israel and Hezbollah. Hezbollah, however, stopped short of their characteristic calls for revenge in the wake of the killings.

Battered by the deadliest war with Israel in decades, experts say the group has little impetus to reignite a conflict that would only weaken the group further as it attempts to recover. Instead, Hezbollah called on the international community in a statement to “assume its responsibilities” and pressure Israel to “withdraw completely from our lands.”

But even as each side accused the other of reneging on their deals, analysts said, both Israel and its opponents had reasons to remain flexible and temporarily overlook the other’s transgressions.

Hezbollah, though angry at Israel for keeping troops in southern Lebanon, would risk a devastating Israeli counterattack if it renews its rocket strikes on Israeli cities. Hamas wants to retain power in Gaza and risks losing it if war returns. And Israel needs to maintain the current arrangement in Gaza long enough to free at least two dozen more hostages. Israeli leaders have also appeared eager to placate President Trump, who campaigned on a promise to keep peace in the Middle East.

Illustrating their desire to prolong the Gaza truce, Israel and Hamas seemed to resolve the weekend’s crisis close to midnight on Sunday. The government of Qatar, a mediator between the sides, said that the female hostage, Arbel Yehud, would be freed this week along with two others who would be released ahead of schedule. In return, Israel said that it would allow displaced Palestinians to return to northern Gaza on Monday morning.

As for Lebanon, the White House announced that the truce there would be extended until Feb. 18, though there was no immediate comment from Israel or Hezbollah. The Lebanese prime minister’s office confirmed the extension.

Aaron David Miller, a former U.S. negotiator in Middle East peace talks, said, “They’re going to get through the next few weeks — beyond that is anyone’s guess.”

“These are not agreements between the United States and Switzerland. They’re agreements that depend on each side giving the other a certain discretion and margin for maneuver,” he added. “That is their weakness, but also their strength.”

That wriggle room ultimately allowed both truces to survive the weekend, even as Israeli troops shot and killed people in both Lebanon and Gaza who were trying to return to areas still controlled by Israel.

The Lebanese Health Ministry said that 22 people had been killed by Israeli fire in southern Lebanon, and the Palestinian Authority’s news agency said that one person had been killed in Gaza as large crowds in both places gathered near Israeli troops, demanding to go home.

But by Monday morning, the standoff in Gaza appeared set to ease. In Lebanon, Hezbollah issued a statement praising the residents attempting to return and calling on foreign powers to force Israel to withdraw. But Hezbollah did not resume its rocket fire.

Analysts say that Hezbollah is unlikely to risk further losses while its leadership is decimated and its benefactor, Iran, is weakened. Also, the group’s main arms supply route, through Syria, was blocked in December when the Syrian president, Bashar al-Assad, an ally of Hezbollah, was ousted by rebels.

Hezbollah’s commanders do “still have some rockets, they have some guns, they can do something,” said Hanin Ghaddar, a Lebanese analyst at the Washington Institute for Near East Policy, a foreign affairs research group.

“But it’s suicidal if they do this, because they know that any kind of attack by Hezbollah in Israel means that Israel will take the opportunity to come back full blast and annihilate whatever is left of them,” Ms. Ghaddar added.

Hezbollah is also probably wary of losing support among its Shiite Muslim base, particularly in next year’s parliamentary elections, Ms. Ghaddar said. Lebanon’s Shiite community paid the largest price for Hezbollah’s decision to go to war with Israel in October 2023 in solidarity with its ally Hamas. Shiite villages and towns in southern Lebanon bore the brunt of Israel’s ensuing air campaign and ground invasion.

“If the Shia do not vote for them, this is the end of Hezbollah,” said Ms. Ghaddar, the author of a book about Hezbollah’s relationship with its base. “They cannot really do anything if they don’t know 100 percent that the Shia community is going to support it.”

Because Hezbollah is less likely to resume fighting, the Gaza cease-fire is considered the frailest of the two truces.

But its biggest stress test is not expected until the beginning of March, when Hamas and Israel must decide whether to extend the arrangement beyond an initial 42-day truce.

For now, Israel has signaled it wants to maintain the cease-fire to sustain the flow of hostage releases. But an extension would require both sides to agree to a permanent end to the war — a bridge that Prime Minister Benjamin Netanyahu of Israel has appeared unwilling to cross. Mr. Netanyahu’s coalition government relies on far-right lawmakers who seek permanent Israeli control of Gaza, and his administration could collapse if the war ends with Hamas still in charge.

The terms of the agreement allow for some flexibility. The truce can continue beyond the 42-day mark as long as both sides remain negotiating about whether to make the arrangement permanent.

But Israeli officials say they will not remain locked in endlessly fruitless negotiations, especially if Hamas stops releasing hostages. And Hamas is unlikely to keep freeing the hostages, its main bargaining chip, without an Israeli promise to cease hostilities permanently.

“Hamas wants a cease-fire but not at all costs,” said Mkhaimar Abusada, a Palestinian political scientist from Gaza. “They want a cease-fire that ends the war.”

Much could depend on President Trump’s willingness to cajole Mr. Netanyahu toward a more lasting truce. Mr. Trump’s private messages to the Israeli prime minister were crucial to the forging of the initial phase, but it remains to be seen whether the American president will maintain that position beyond a few weeks.

“If Netanyahu succeeds in convincing Trump of the need to renew the war, there’ll probably be a renewal of the war,” Mr. Abusada said. “If Trump keeps his promise that he doesn’t want any wars and he wants more peace — whether it’s in Gaza, Ukraine or all over the world — that’s a different thing.”

Ms. Yehud is the last female civilian hostage that Israel believes is most likely alive. Another civilian woman, Shiri Bibas, remains in Gaza after she was abducted from Nir Oz with her two young sons, Ariel, who was 4 at the time, and Kfir, who was 9 months. The Israeli military has expressed grave concern for the lives of Ms. Bibas and her children, though their deaths have not been confirmed.

Ms. Yehud’s brother, Dolev Yehud, was missing for months and was also assumed to have been kidnapped. It later became clear that he never made it into Gaza: In June 2024, the Israeli authorities declared him dead after his remains were identified in Nir Oz through new testing.

Under the terms of the cease-fire deal, Ms. Yehud should have been among the first two groups of hostages released on Jan. 19 and Jan. 25, according to the Israeli authorities. Israel had demanded that its female civilians be released before the captive female soldiers, four of whom were released on Saturday.

It appears Ms. Yehud may be in the custody of another group, Palestinian Islamic Jihad. An official with that group told The New York Times on Sunday that she would be released before next Saturday.

Just after midnight on Monday, Israel, Qatar and Hamas announced that a resolution had been finalized for the release of Arbel Yehud and two other Israeli hostages by next Friday, with three more hostages to be released on Saturday. In exchange, Israel would begin allowing Palestinians in Gaza who had been displaced to return to the north of the enclave, the officials said.

Ms. Yehud has deep roots in the community of Nir Oz as a third-generation member of her family to reside there, according to the Hostages and Missing Families Forum, a grass-roots organization that advocates for the release of the hostages. She worked in the community’s education system before becoming a guide at GrooveTech, an innovative learning center in southern Israel that focuses on space exploration and technology.

Ms. Yehud and Mr. Cunio had returned from a tour in South America shortly before the 2023 attack, according to the forum.

Nir Oz has become a symbol of the Israeli military, intelligence and government debacle that led up to the attack and failed to protect the country’s citizens that day. It was a small kibbutz, or communal village, of roughly 400 people before the attack, during which more than a quarter of its population were killed or kidnapped.

Speaking at a protest on behalf of the female hostages in New York in December, Lian Weiss, a relative of Ms. Yehud, pleaded for their release. “Please close your eyes for a moment and imagine: Imagine it is you. You are ripped from your home,” she said, adding, “We cannot let this become their forever. Every moment we delay is another moment of agony for these women. We must act. We have the power to change their fate.”