Negotiators meet to revive the push for hostage release and a cease-fire in Gaza.

Senior officials from Israel, Egypt, Qatar and the United States met in Rome on Sunday to continue negotiations over a cease-fire in Gaza, according to three officials involved in or briefed on the talks and a statement from the Israeli government. The talks came as tensions mounted in the region amid growing violence along the border between Israel and Lebanon.

The officials at the daylong talks in Rome were pushing to forge a truce in which Israeli hostages held captive by Hamas would be exchanged for hundreds of Palestinians jailed by Israel under a plan that has been discussed for months. Qatar hosts part of the Hamas leadership and, along with Egypt, plays a key role in mediating between the two sides.

The Israeli government announced on Sunday evening that its representative at the meeting, David Barnea, Israel’s foreign intelligence chief, had already returned home and that negotiations would resume in the coming days. The statement did not give further details.

Despite progress in recent weeks, the monthslong negotiations remain stalled over several critical issues, particularly the extent to which Israeli forces would remain in Gaza during a truce, according to seven officials involved in or briefed on the talks.

Earlier in July, Israel hardened its position on maintaining checkpoints along a strategic highway south of Gaza City, weeks after suggesting that it could compromise. It was unclear on Sunday if Mr. Netanyahu had allowed negotiators to show greater flexibility on the matter during the talks. Mr. Netanyahu faces pressure from members of his right-wing government to stick to a tougher line.

The length of the truce is also a source of dispute: Hamas wants a permanent truce, while Israel wants the option to resume fighting.

Israel has also refused to guarantee that its troops will leave the Gaza-Egypt border during a cease-fire, fearing that Hamas would smuggle arms across the frontier in the absence of Israeli forces.

Israeli negotiators have privately discussed leaving the border zone if they can first install electronic sensors to detect future efforts to dig tunnels, as well as construct underground barriers to block tunnel construction, according to three officials briefed on the talks. But no agreement has been reached, the officials said.

Israel wants to maintain military checkpoints along a strategic highway inside Gaza in order to prevent Hamas fighters from ferrying weapons toward Gaza City, according to four Israeli officials and an official from one of the mediating countries. After appearing more flexible on the issue earlier in the summer, Israel’s stance hardened again roughly three weeks ago, while Hamas never agreed to compromise, the officials said.

All the officials spoke on condition of anonymity in order to speak more freely about sensitive matters.

The meeting in Rome came as Western diplomats scrambled on Sunday to prevent a surge of fighting along the Israel-Lebanon border, officials said, after a rocket from Lebanon on Saturday killed at least 12 people in an Israeli-controlled town, most of them children. Israel retaliated early Sunday with strikes across Lebanon.

Before the latest strikes, mediators between the two sides had been hoping that a truce in Gaza could provide the impetus for an easing of tensions along the Israel-Lebanon border, even as the risk of escalation there remains higher than ever.

Six Israeli officials said that Prime Minister Benjamin Netanyahu was the main reason for Israel’s hardened stance at the Rome talks, and that top security officials are pushing for the prime minister to show greater flexibility in order to secure a deal. Mr. Netanyahu’s room for maneuver is limited by the members of his right-wing coalition government; some of them oppose a truce that would allow Hamas to survive the war intact and have threatened to bring down the government if their wishes are not met.

Mr. Netanyahu’s office did not respond to requests for comment. But on Thursday, he promised families of hostages held in Gaza that his government would not introduce new conditions or obstacles to achieving a framework agreement for a cease-fire, according to Jonathan Dekel-Chen, whose son Sagui was abducted during the Hamas-led Oct. 7 attack.

Mr. Netanyahu’s pledge, Mr. Dekel-Chen said, was made in the presence of President Biden, his national security adviser, Jake Sullivan, and six families with relatives held in Gaza.

“He committed in front of the president to act with more urgency than he has in the past,” Mr. Dekel-Chen said in a phone interview on Saturday.

The talks in Rome came as tens of thousands of people have been forced under Israeli orders to evacuate several neighborhoods in southern and central Gaza, according to the United Nations.

An Israeli order on Saturday was the latest in a series of such directives recently that have forced displaced Palestinians to again relocate.

The order includes an area around the city of Khan Younis that Israel had previously designated a “humanitarian zone” for Palestinian civilians, who have faced nearly a year of unrelenting war and struggled to avoid disease and find food and clean water.

Tens of thousands of people have been heading on foot toward Al Mawasi, an already overcrowded stretch of tents near the sea in Gaza that has served as a makeshift refuge of last resort for months. About 182,000 people were displaced from the southern city of Khan Younis to Al Mawasi in just a few days last week, the United Nations estimates.

But the United Nations also said hundreds remained stranded in areas that had been ordered evacuated, including about 300 sheltering at various schools.

Some were forced to stay because of disabled relatives. Kamel Abu Jamea, 73, a Khan Younis resident, said his wife, Amna, 73, was too sick to walk, leaving them unable to evacuate despite the shelling and gunfire he could hear outside. He had tried to find a ride for them to a safer area, but had no luck. And their food, water and medication were all running out.

“My wife can’t even walk five meters,” he said. “I can’t leave her and go.”

The Israeli evacuation orders have further complicated the work of aid groups trying to serve the Khan Younis area.

Twelve distribution points that had been set up to give out food have suspended their operations, along with eight hot meal kitchens and nutrition programs for children and pregnant women at two shelters, the United Nations said. Ten water and sanitation facilities, and at least 17 shelters have also stopped working, it said.

Vivian Yee contributed reporting from Cairo, and Iyad Abuheweila from Istanbul.