Egypt is in talks with Israel to reopen the Rafah border crossing with Gaza as part of a new effort that could allow more aid to flow into the enclave and create movement toward a broader deal to halt the fighting there, Arab peace negotiators say.

Egyptian officials were in Israel earlier this week to negotiate terms for the reopening of the crossing, which was heavily relied upon for aid delivery and distribution but has been shut since May, when Israel launched a large-scale military operation in the Gaza border town of Rafah.

The new plan aims to build on the momentum generated this week by the cease-fire in Lebanon , which broadly held for a fourth day Saturday after two months of fierce fighting between Israel and Hezbollah.

If Egypt and Israel agree, the crossing could open as soon as early December, according to the Arab negotiators. The fresh push to reopen the crossing is part of a new proposal being discussed with both Israel and Hamas to halt the fighting in Gaza for at least 60 days and allow Israel to maintain a military presence in the enclave. Hostages held in Gaza would begin to be freed after seven days.

Hamas officials were expected to discuss the new proposal in Cairo on Saturday, the negotiators said. A Hamas official confirmed that a delegation was going to Cairo but declined to comment on its agenda.

Hamas expressed openness to a cease-fire on Wednesday when it commented on the agreement reached in Lebanon, but has long resisted conditions that are important to Israel.

The cease-fire in Lebanon, however, has taken Hamas’s ally Hezbollah out of the fray, leaving Hamas isolated and weakened after Israel killed many of its top officials and operatives, including leader Yahya Sinwar in October.

Egypt and Hamas have both indicated that they won’t insist on the Israeli military leaving the Gaza side of the Rafah border crossing immediately, in a U-turn over a key demand that had scuttled previous attempts to reopen the crossing.

The Israeli Prime Minister’s Office declined to respond to a request for comment.

Israeli Prime Minister Benjamin Netanyahu told Israeli media Thursday that he isn’t prepared to end the war in Gaza. On Tuesday, he said Israel would “complete the task of obliterating Hamas.”

Netanyahu’s hard-line coalition members have for months threatened to undermine the stability of his government if the prime minister signs a cease-fire agreement that ends the war without destroying Hamas, but he is coming under renewed pressure from families of hostages held in Gaza and the Biden administration in the wake of the Lebanon agreement.

The deal in Lebanon put a spotlight on the dire conditions in the Gaza Strip, where more than a year of fighting has left much of the enclave in ruins, displaced the bulk of the more than two million people living there and killed more than 44,000 people, according to Palestinian health authorities, who don’t say how many were combatants.

Much of Gaza’s physical infrastructure is destroyed. Squalid conditions, made worse by reduced access to clean water, have raised fears of the spread of infectious disease , leading to a mass polio vaccination campaign this fall as one case was reported in the enclave. Food insecurity remains high as most people are displaced and aid convoys are threatened by looters and face security restrictions on their movement.

The war was triggered by the Hamas-led attacks on southern Israel that on Oct. 7, 2023, left 1,200 people dead and around 250 taken hostage. Around 100 hostages remain in Gaza, though many of them are suspected to be dead.

Months of diplomatic efforts led by the U.S. to reach a deal to stop the violence and free the remaining hostages have come up empty amid deep disagreements over whether Israeli troops can remain in Gaza and whether there should be a permanent end to the fighting.

Under the proposal to reopen the Rafah crossing, the Palestinian Authority, a Hamas rival that administers parts of the West Bank, would help run the Palestinian side of the crossing, with Hamas completely relinquishing control. Israel would screen the names of people going through the crossing.

In the beginning stages, 200 aid trucks would be allowed to enter Gaza each day, according to the Arab negotiators.

“Nothing is confirmed for now,” said a senior Palestinian Authority official, through a spokesman. The U.S. State Department declined to comment.

The International Court of Justice , the top United Nations tribunal, ordered Israel earlier this year to allow greater aid flow into the enclave and to reopen the Rafah land-border crossing. The International Criminal Court, a tribunal separate from the ICJ focused on individuals that is also located in The Hague, issued arrest warrants against Netanyahu and former Defense Minister Yoav Gallant last week, accusing their government of enacting policies aimed at intentionally starving Palestinians. Israel and both leaders have strongly opposed the charges.

Gaza talks have become moribund as the region’s attention shifted to Lebanon and Israel pressed an operation in the northern part of the enclave to kill remnants of Hamas that had reorganized there. The fighting and besiegement, along with colder weather, have left residents facing dire conditions.

Complicating humanitarian response efforts, Israel has intermittently asserted that some aid-organization local staff are enmeshed to some degree with militants. Israel on Saturday said it killed a Palestinian working for the World Central Kitchen aid group, after determining that the man took part in invading a hard-hit Israeli community on Oct. 7 last year. Palestinian media claimed that a strike on a car in Khan Younis that killed the man killed additional people, as well.

WCK said it would pause its Gaza operations in the wake of the strike. It said it didn’t have knowledge of whether its employee was involved in the Oct. 7 attack on Israel last year. Israel called on the organization to do an investigation into its employees.

WCK was one of the main international organizations delivering food aid in Gaza when an Israeli strike killed seven of its employees in April . Israel’s military deliberately targeted WCK’s convoy in a case of mistaken identity, after spotting what looked like armed men in their vehicles and thinking the convoy was linked to Hamas. Israel apologized for the incident, which drew widespread international condemnation.

Egypt in October proposed a small-scale cease-fire of up to two weeks in hopes of building momentum for a larger deal, mediators said at the time. Israel has separately offered Hamas members safe passage to another country if they stop fighting and release the hostages. Hamas, a U.S.-designated terrorist group, swiftly rejected the offer.

—Carrie Keller-Lynn, Anat Peled and Saleh al-Batati contributed to this article.

Write to Summer Said at summer.said@wsj.com and Omar Abdel-Baqui at omar.abdel-baqui@wsj.com