JERUSALEM — For Gazans and Israelis yearning for a cease-fire and a deal to free hostages, feelings of cautious optimism have been dashed so many times that any optimism now seems incautious.

Once again, attention has turned to talks in Cairo amid reports that an agreement may be within reach. Once again, leaks from the parties are contradictory and hard to interpret, with hopeful signals quickly scrambled by dour assessments.

Egyptian officials have suggested that the basics of a deal are nearly settled. Israeli Foreign Minister Israel Katz said Monday that negotiations have reached a “critical point.” Hamas dismissed the terms on the table as “nothing new,” but the Palestinian militant group also said it would “review the proposals.”

What appeared different this time, experts said, were the new pressures at play, particularly on Israel, with Washington’s impatience with Prime Minister Benjamin Netanyahu nearing a breaking point just as domestic anger in Israel is surging.

On March 25, the United States stood aside to allow the U.N. Security Council to pass its first resolution calling for a cease-fire in Gaza. A week later, Israeli forces killed seven World Central Kitchen humanitarian workers, sparking another wave of condemnation. Israel’s military said the strike was a mistake and dismissed two of the officers involved.

In Israel, frustrations with the prime minister from both hostage families and Israel’s democracy movement have converged into massive anti-government protests. Opposition leader Benny Gantz, who serves in the emergency war cabinet and has emerged as a popular alternative to Netanyahu, called last week for elections in November.

The mounting pressure has shifted thinking inside Netanyahu’s office, according to an Israeli familiar with the deliberations. Among the changes is a recognition that the prime minister’s standoff with President Biden over the course of the war and the delivery of humanitarian aid may have backfired, and that domestic fury over the fate of the more than 100 remaining hostages can no longer be kept at bay.

“The difference now is that all the elements are pushing for a deal to happen,” said the Israeli familiar with the deliberations, who spoke on the condition of anonymity to describe confidential discussions. Netanyahu “really does need to make a significant achievement with a deal.”

Netanyahu’s circle hopes that an agreement now could revive chances of a diplomatic rapprochement with Saudi Arabia — which Washington had been attempting to broker before the Gaza war — and reverse the prime minister’s political free fall.

Shifts have been evident on the ground in Gaza, as well. Israel promised last week to open an additional crossing for aid to the northern Gaza Strip, and Sunday pulled most of its troops from the south. The stated reason was to rest the units for future action, including an attack on Rafah — Hamas’s final redoubt, where more than a million civilians are sheltering. But the withdrawal, leaving only a few thousand troops along an east-west corridor dividing the enclave, was widely seen here as a concession before negotiations.

“The return of Palestinians to the north is a sticking point,” said Michael Horowitz of Le Beck International, a security firm. “This is a fairly big compromise.”

Israeli negotiators last week were given their most wide-ranging mandate yet to reach a deal, according to local media reports. And senior officials have been unusually bullish about the prospects for a breakthrough.

Katz, the foreign minister, suggested it was the closest the sides had been “since the first deal,” reached in November, which involved the release by Hamas of 105 Israeli hostages and foreign nationals in exchange for 240 Palestinian prisoners in Israeli jails.

“If matters work out, a large number of hostages will return home and, in stages, everyone,” Katz told Israel’s Army Radio.

An unidentified Israeli negotiator described “significant progress” in Cairo Monday night, according to Israel’s Channel 13, with negotiators potentially willing to bargain on withdrawing more troops and allowing civilians to return to the north.

“We are ready to make difficult decisions in order to get the hostages back,” Israeli Defense Minister Yoav Gallant said in an address to troops at a military base Monday. “I think that we are at a good point for a deal.”

But the forces pushing against an agreement are also strong. Netanyahu’s far-right allies have made it clear that a cease-fire could fracture his coalition, endangering his tenuous hold on power. National Security Minister Itamar Ben Gvir said Monday on X that halting the war without a final push in Rafah would erase Netanyahu’s “mandate to serve as Prime Minister.”

The United States is trying to pressure both sides to overcome the barriers to a deal. Military analysts said the withdrawal of Israel’s 98th Commando Division from Khan Younis could allow Qatar and Egypt to press Hamas for concessions.

The drawdown is “tied to the sense that the U.S. is putting a lot more pressure on mediators to, in turn, pressure Hamas to agree to a deal,” Horowitz said.

The Biden administration has attempted to jump-start stalled talks for months. CIA Director William J. Burns has bounced between Paris, Cairo, Qatar and Tel Aviv. Mediators, technical teams and negotiators have met nearly a dozen times this year.

Gershon Baskin, who helped negotiate the release of captured Israeli soldier Gilad Shalit from Hamas captivity in 2011, said the deal reached in November was easier because it focused on the release of women and children on both sides.

“The first round was the low-hanging fruit. It was a no-brainer,” he said.

The current round is more complex because Hamas considers most of the remaining hostages to be combatants and has demanded greater concessions. The demands, according to diplomats familiar with the talks, include a complete Israeli troop withdrawal, the return of displaced Gazans to their homes in the north and the restoration of food deliveries to prewar levels of about 500 trucks a day.

In the case of Shalit, Baskin said that the basic terms were set quickly but that it took five years for the two sides to agree on the details.

“What does take time are the logistics,” Baskin said, which in this case will include the mechanics and monitoring of the hostage transfers. “We haven’t even gotten to the logistics issues in these talks yet.”

The latest proposal under discussion would see 40 Israeli hostages exchanged for 900 Palestinians in Israeli prisons, 100 of whom are serving terrorism sentences, according to a former Egyptian official, who spoke on the condition of anonymity to discuss the talks. Disagreements remain about which prisoners would be freed; it is also unclear how many of the hostages are still alive.

There has been a burst of activity on the U.S. side in recent weeks, according to the former official. Biden contacted Egyptian President Abdel Fatah El-Sisi and the emir of Qatar, urging the Arab countries to press Hamas harder for a deal.

“We are trying to put a lot of pressure on Hamas. The problem is Sinwar is in Gaza and the other [Hamas leaders] live in Qatar,” the former Egyptian official said, referring to Hamas leader Yehiya Sinwar, who is widely believed to be hiding in tunnels below Gaza and to have the final say on any agreement. “The decision comes from Sinwar.”

U.S. officials characterized the Cairo talks, led by Burns, as “serious.”

“A proposal was submitted to Hamas, and now it’s going to be up to Hamas to come through,” National Security Council spokesman John Kirby said Monday.

George reported from Dubai and Parker from Cairo. Loveday Morris in Berlin and Karen DeYoung in Washington contributed to this report.

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