Israel’s foreign minister said on Wednesday that there were encouraging signs in the U.S.-led efforts to restart intensive cease-fire negotiations with Hamas, adding that Israel was eager for talks to resume “as soon as possible.”

The remarks by the minister, Gideon Saar, came one day after President Trump said Israel had agreed to “conditions to finalize” a 60-day cease-fire with Hamas, which would free some of the hostages still in Gaza.

“There are some positive signs,” Mr. Saar told reporters at a news conference in Estonia, part of a diplomatic tour of three E.U. members in the Baltics. “But our goal is to begin proximity talks as soon as possible,” he added, referring to the mediated shuttle diplomacy needed to flesh out details of the agreement.

Hamas said on Wednesday that it was considering the new proposal.

The momentum toward new talks picked up just ahead of the planned meeting between Prime Minister Benjamin Netanyahu of Israel and President Trump next week in Washington. And it followed the recent decision by the United States to join Israel in bombing Iranian nuclear sites.

Mr. Trump, who has voiced increasing frustration with what he has labeled “this very brutal war” in Gaza, says he hopes to see a cease-fire reached as soon as next week.

The exact terms of the new proposal remained unclear on Wednesday. The two sides would need more talks to work out the details of a potential truce, let alone a permanent cease-fire.

But according to an Israeli defense official and a Palestinian close to Hamas, the deal would entail the release of 10 of the remaining living hostages and the return of 18 bodies still held by Hamas in Gaza in exchange for Palestinian prisoners. Both were briefed on details of the evolving agreement and spoke on condition of anonymity to discuss sensitive diplomacy.

The release of the hostages and the return of the bodies would be staggered, with five groups over the 60-day period, they said. That was a change from what was outlined in a U.S. proposal in May, under which all captives would have been released by the seventh day of the cease-fire.

Hamas would also refrain from holding televised handover ceremonies like those it staged when releasing hostages during the two-month truce that began in January, the two sources said. The events — in which Israeli hostages were often made to give speeches thanking their captors — drew international criticism.

Three Israeli officials, who spoke on condition of anonymity to discuss sensitive diplomacy, also said the latest effort aimed to offer Hamas stronger assurances that the temporary truce could carve out a path toward a permanent cessation of hostilities.

While some officials were suggesting that Israel had softened its position, Mr. Netanyahu vowed again in a speech on Wednesday to “fundamentally eliminate” Hamas.

“I am telling you — there will be no more Hamas,” he said. “We are not going back to that.”

Though Israeli officials were cautiously optimistic on the state of the talks, it was not clear whether the latest formula would overcome the sticking points that have consistently dogged the negotiations to end the war.

Mr. Netanyahu has said that he is ready for a temporary cease-fire, but that he will not permanently stop the war unless Hamas ends its rule in Gaza and its leaders go into exile, conditions that Hamas rejects.

Hamas leaders say they will return all remaining hostages — about 20 of living captives and the bodies of about 30 others — only if Israel ends the war permanently.

Moving ahead with the cease-fire talks could also rattle Mr. Netanyahu’s grip on power. His far-right coalition partners, including two senior ministers, oppose ending the war and call for indefinite Israeli rule in Gaza instead.

But some analysts say Mr. Netanyahu may now be ready to change course.

Buoyed by what many Israelis consider his successful June war with Iran, Mr. Netanyahu might now be willing to risk the collapse of his governing coalition — particularly if he can capitalize on an end to the war in Gaza to advance Israel’s diplomatic ties with neighboring Arab countries.

More than 56,000 people, including thousands of children, have been killed in the war in Gaza, according to the Gaza health ministry, which does not distinguish between civilians and combatants.

The war began when Hamas and its allies attacked Israel on Oct. 7, 2023, killing about 1,200 people, mostly civilians. More than 250 others were taken hostage, according to Israel.

Israel and Hamas agreed to two short-lived cease-fires, both of which saw hostages in Gaza swapped for Palestinian prisoners. During the last truce, which Israel ended in mid-March, Israel released more than 1,500 prisoners and Hamas turned over 30 hostages and the bodies of eight more.

Israeli forces kept up attacks across Gaza on Wednesday. In one strike, they killed Marwan al-Sultan, a Gaza doctor who had led the Indonesian Hospital in northern Gaza, according to the Gaza health ministry.

The hospital is currently out of service after Israeli military operations, the health ministry said. The Israeli military did not immediately respond to a request for comment.