JERUSALEM — U.S. and Israeli officials Thursday expressed renewed optimism over a cease-fire deal in the Gaza Strip, after Hamas revised its position and Israeli Prime Minister Benjamin Netanyahu then told U.S. President Joe Biden that he is sending a new delegation of negotiators to the stalled talks.

White House officials said they believed new progress in the talks amounted to what one repeatedly called "a breakthrough" in the monthslong negotiations, although they said that it would take some time to work out the many steps involved in implementing a truce. Israeli and other officials involved in the talks agreed that there had been progress but described it in more cautious terms.

The discussions are based on a three-stage framework deal publicized by Biden in late May and endorsed by the United Nations. If carried out, the agreement would ultimately stipulate an end to the war, a full Israeli withdrawal from Gaza, and for Hamas and its allies to release the remaining 120 living and dead hostages in Gaza for Palestinians held in Israeli jails. A senior Biden administration official directly involved in the talks said there is broad agreement now about the steps required to transition from Phase 1, a temporary cease-fire, to Phase 2, a permanent end to the fighting and a release of the remaining living hostages.

The official, who asked not to be identified because of the sensitivities of the negotiations, compared the current situation to the deal that was eventually reached in November that led to a cease-fire for several weeks and the release of about 105 hostages. He said a "framework is now in place" for a new truce but that there was still more to do to reach a final deal.

The shift followed Hamas' announcement Wednesday that it had "exchanged some ideas" with the mediators on the cease-fire deal after weeks of deadlock. An Israeli official, who spoke on condition of anonymity to discuss the sensitive talks, said Wednesday night that wide gaps between the sides remained but that Hamas' revised position left potential to move forward in the talks.

David Barnea, head of the Israeli Mossad intelligence agency, will lead the Israeli negotiating team in Qatar as soon as Friday, said a second Israeli official and another official familiar with the talks.

Many obstacles remain, including the question of whether Netanyahu will risk his right-wing coalition in agreeing to a cease-fire with Hamas. Two of his far-right coalition partners have insisted that the war against Hamas continue, potentially forcing Netanyahu to choose between a deal that ends the war and frees the hostages, and the survival of his government.

Netanyahu's office said the prime minister reiterated in his call with Biden on Thursday evening that Israel would end the war "only after achieving its goals." Israel's stated goals include destroying Hamas' military and governing capabilities in Gaza, and ensuring that the Palestinian enclave cannot again pose a threat. Both aims could still take substantial time to achieve, if at all.

The cease-fire talks had ground to a halt in June. After Biden announced the proposal, Hamas demanded amendments, leading Israel to quickly declare that Hamas had rejected the deal. The Biden administration said that some of Hamas' demands were unworkable.

The White House, in a statement Thursday, said Biden "welcomed the prime minister's decision to authorize his negotiators to engage with U.S., Qatari and Egyptian mediators in an effort to close out the deal," but made no mention of Israeli caveats.

Efforts to revive the negotiations came amid simmering tensions along Israel's northern border, with the Lebanese armed group Hezbollah launching an unusually large rocket and drone attack toward Israel on Wednesday and an even bigger one on Thursday, in retaliation for Israel's killing of a Hezbollah commander on Wednesday. The rocket barrage killed one Israeli reservist officer and sparked wildfires along Israel's northern border.

The main stumbling blocks in the Gaza talks have been related to a fundamental dispute: Hamas wants guarantees that the deal would lead to an end to the war and a full withdrawal of Israeli forces, while Israeli leaders have vowed to keep fighting until Hamas is destroyed and to keep postwar security control of Gaza in Israeli hands.

According to two senior officials briefed on the talks, recent disagreements had largely centered on two paragraphs in the proposed agreement, both related to negotiations on a permanent truce. Those negotiations would take place during the first phase of the deal, a proposed six-week cease-fire, during which some hostages would be exchanged for Palestinian prisoners.

Hamas wanted to limit those talks to the number and identity of Palestinian prisoners to be released for each remaining hostage, while Israel wanted to leave it open-ended, so more topics could be added into the discussions, according to the two senior officials.

Hamas feared Israel might torpedo the talks by expanding them to deal with other, effectively unresolvable issues, which would allow Israel to continue the war, the officials said. Qatari negotiators offered Hamas three potential alternatives last week, according to the two senior officials, although they did not give further details.

The proposal also stipulates that if Israel and Hamas cannot reach a deal on a permanent cease-fire before the six-week truce expires, negotiations will continue until they do. The two senior officials said Hamas wanted language that guaranteed Israel could not unilaterally declare that the talks had collapsed and return to battle.

Some influential members of Netanyahu's coalition government have expressed opposition to a potential deal with Hamas.

"Now is not the time to stop, it is entirely the opposite: It is the time to bring in more forces and increase our military pressure," Bezalel Smotrich, the country's far-right finance minister, said Tuesday. "It would be absurd if we were to stop just a moment before success — the end, total victory over Hamas."

The Biden administration hopes that a truce in Gaza will allow Israel and Hezbollah, which has been firing at Israel in solidarity with Hamas, to reach a diplomatic settlement as well.

On Thursday, Hezbollah launched one of the largest attacks on northern Israel since the war in Gaza began, triggering air-raid sirens across the area for over an hour and sending thousands running for fortified shelters. Roughly 200 rockets and mortars and 20 drones were launched into northern Israel, according to the Israeli military.

Since the Hamas-led attack on Israel on Oct. 7, Hezbollah, the politically powerful Lebanese armed group, has repeatedly attacked northern Israel in solidarity with Hamas, prompting Israeli strikes in Lebanon. More than 150,000 people on both sides of the Israel-Lebanon border have fled, with little idea of when they might return home.

Hezbollah said Thursday's barrage was partly a response to Israel's assassination of a senior Hezbollah military commander the previous day in the region of Tyre in southern Lebanon. But the Hezbollah munitions were mostly fired on border areas, avoiding a broader attack on Israel's heartland that would most likely have provoked a more severe response.

Hezbollah has said its forces will not stop their attacks until Israel ends its military campaign in Gaza. At the same time, Israeli officials have voiced increasingly bellicose threats of a potential invasion of Lebanon to push Hezbollah away from the border.

This article originally appeared in The New York Times.