Israeli negotiators traveled to the Gulf nation of Qatar on Friday for the first time in weeks to restart talks over a cease-fire deal that would end the war in Gaza and free the hostages held there, following weeks of deadlock in the negotiations.

David Barnea, the head of Israel’s Mossad foreign intelligence service, led the Israeli delegation to Doha, the Qatari capital, and met with Mohammed bin Abdulrahman bin Jassim Al Thani, the Qatari prime minister, according to an official familiar with the visit.

Cease-fire negotiations had been stalled for weeks until Wednesday, when Hamas announced that it had exchanged some ideas with mediators on a new way forward. Both U.S. and Israeli officials said the revised Hamas position could allow for an agreement, but cautioned that a protracted and difficult series of deliberations lay ahead nonetheless.

“The head of the Mossad returned a short while ago from an initial meeting with the mediators in Doha,” the office of Israel’s prime minister, Benjamin Netanyahu, said in a statement on Friday night. “It was decided that next week a delegation will head out to continuing the negotiations. It is emphasized that gaps still exist between the sides.”

Both sides would have to sort out the identity, number and conditions for the release of Palestinian prisoners who would be freed in exchange for the 120 living and dead hostages held by Hamas and its allies. They also would have to determine a sequence of steps for Israeli military withdrawal and how much control Israeli forces would have at different phases in the agreement.

Most critically, Israel and Hamas would have to agree on a formula to resolve the major sticking point that has thwarted talks for months: Hamas has demanded nothing less than a complete cease-fire and a full withdrawal of Israeli forces, while Israel has vowed to topple Hamas’s rule in Gaza and maintain postwar security control of the territory.

Israel and Hamas have been negotiating on the basis of a three-stage cease-fire framework publicized by President Biden in late May. The two sides refuse to talk directly, requiring Qatari and Egyptian mediators to conduct shuttle diplomacy between them.

Under the terms of the proposed deal, they would first observe a six-week truce during which hostages would be released in exchange for Palestinian prisoners. During those six weeks, officials would negotiate an end to the war and the withdrawal of Israeli troops from Gaza.

Prime Minister Benjamin Netanyahu of Israel has vowed to destroy Hamas’s “military and governing capabilities” in Gaza and still says the war will not end until that goal is achieved. But Israel’s military establishment — worn down by the ongoing war in Gaza and weighing the possibility of a large-scale fight with Hezbollah in Lebanon — now backs a cease-fire deal even at the cost of leaving Hamas in power.

Michael Milshtein, a former Israeli intelligence officer, said Israel was not going to successfully topple Hamas, leaving a cease-fire deal to bring home the remaining hostages as the least bad outcome.

“It is an extremely difficult pill to swallow,” said Mr. Milshtein, who oversaw the Palestinian affairs division in Israeli military intelligence. “But there are no good alternatives here.”

Israel’s political leaders, however, are deeply divided on the proposed deal, which some argue would effectively leave Hamas in power in Gaza. Although the top Israeli leadership has given a green light to the framework deal, two senior members of Mr. Netanyahu’s coalition have vowed to oppose it, threatening to bolt from the government, potentially forcing him to choose between a cease-fire and his political survival.

On Friday, Benny Gantz, an opposition leader who recently quit Mr. Netanyahu’s war cabinet, reiterated that he would back the prime minister if he decided to advance a cease-fire deal to release hostages. In that case, Mr. Netanyahu would be forced to rely on his rivals for support, a combustible situation that would almost certainly push the country toward elections.

Mr. Netanyahu did not unequivocally endorse the proposal for weeks. In a television interview last month, he appeared to walk back his support for it, saying he would not countenance an end to the war against Hamas. After an outcry from the families of hostages, Mr. Netanyahu zigzagged and publicly backed the proposal in late June.

Hamas faces a similarly complex calculus.

In a statement on Friday, Hamas called on all Arab and Muslim countries to pressure Israel into ending the “Zionist genocide against our Palestinian people.”

The group also reiterated its rejection of any plans or proposals that would bring foreign forces into the Gaza Strip. The ideas of an Arab peacekeeping force and more recently, a U.N. peacekeeping force, have been floated as possible solutions to help bring an end to the war and Israel’s occupation of Gaza.

“The administration of the Gaza Strip,” Hamas said in its statement, “is a purely Palestinian matter, agreed upon by our Palestinian people in all their diversity.”

Some Gazans increasingly criticize the armed group for launching the Oct. 7 attack on Israel, which triggered the war, without doing enough to protect Gazan civilians. And any agreement would need the blessing of the Hamas leader inside Gaza, Yahya Sinwar, whom Israel has vowed to kill for his role in the surprise assault.

Ahmed Yousef, a veteran Hamas member, blamed Israel’s hard-line government for the delay in achieving a cease-fire deal in Gaza. But he said many would likely argue the war had not been worth the heavy price paid in Gaza, even should an agreement see Israel release thousands of Palestinian prisoners in exchange for the remaining hostages.

“Even if many prisoners are freed, no one is going to say that there was any achievement,” said Mr. Yousef, himself now displaced in southern Gaza.

Turkish President Recep Tayyip Erdogan told journalists on Friday that Western countries needed to exert collective pressure on Israel to achieve a definitive cease-fire. He added that he hoped President Joe Biden’s intervention and Qatar’s mediation efforts would lead to a lasting truce.

While leaders on both sides weigh the path forward, Israel’s war in Gaza neared the end of its ninth month. The vast majority of the population has been displaced at least once, with many living in tents, and finding enough food and water to survive has become a daily struggle.

On Friday, Israeli forces continued to fight in Shajaiye, a neighborhood near Gaza City in the north of the territory, in an attempt to crack down on Palestinian militants there. The Israeli military has increasingly doubled back to areas of Gaza that its forces first swept through months ago, as it battles renewed insurgencies by Hamas and other armed groups.

“The military can talk all it wants about having dismantled battalions — but at the end of the day, Hamas has survived,” said Mr. Milshtein. “We can tell ourselves stories all day long, but this is not even close to the so-called total victory over Hamas.”

Raja Abdulrahim contributed reporting from Jerusalem.