The White House says talks to reach a cease-fire in the Gaza Strip and free Israeli and foreign hostages held by Hamas militants are nearing their end-stage and could result in a deal by next week.

President Biden said on Friday the two sides are “closer than we’ve ever been” to a deal.

“I don’t want to jinx anything. But as my grandfather said, ’With the grace of God, the goodwill of the neighbors, and a lot of luck, we may have something,” Mr. Biden said. “But we’re not there yet. But we’re much, much closer than it was three days ago. So keep your fingers crossed.”

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The president expressed optimism after two days of talks in Doha, Qatar, among U.S., Qatari and Egyptian officials. Israel sent negotiators while Palestinian militants in Hamas sent messages through mediators. Both Israel and Hamas accuse the other side of seeking new conditions on the outline of a cease-fire deal Mr. Biden unveiled earlier this year in a bid to stop more than 10 months of fighting.

A senior administration official said negotiating teams tried to bridge gaps in negotiations and will resume talks in Cairo next week “to close out this process once and for all.”

“We aim to conclude this deal,” the official said. “There’s momentum here in this process.”

In a related move, the State Department announced Friday afternoon that Secretary of State Antony J. Blinken would travel to Israel Saturday “to continue intensive diplomatic efforts to conclude the agreement for a cease-fire and release of hostages and detainees through the bridging proposal presented today by the United States, with support from Egypt and Qatar.”

Mr. Blinken, who has made multiple trips to the region since the war began and has been on the phone with officials around the region in recent days, “will underscore the critical need for all parties in the region to avoid escalation or any other actions that could undermine the ability to finalize an agreement.”

Hamas killed some 1,200 people and took hundreds of military and civilian hostages in deadly raids on southern Israel on Oct. 7, leading to an aggressive military reprisal by Israel on Hamas-controlled Gaza.

Roughly 100 hostages were freed last year but over 100 remain, enduring months of captivity. It is unclear how many hostages remain alive.

Tensions have spiraled, including between Israel and Iran-backed Lebanese militants, triggering fears Tehran will take a bigger role in the violence and spark an all-out war in the region.

Mr. Biden has been walking a fine line, reiterating U.S. support for Israel while pressing it to de-escalate tensions and reduce civilian deaths in Gaza. Prime Minister Benjamin Netanyahu has insisted the fighting will not fully stop until Hamas is defeated as a military threat to Israel.

U.S. officials say unfolding talks may be the last chance they have to end the violence in Gaza while ensuring the hostages’ safety.

“There’s really a new spirit here to drive this to a conclusion,” the official said from Qatar. “We have to get the hostages out.”

• David R. Sands contributed to this story.