Netanyahu slams his defense minister for questioning the goal of ‘total victory’ in Gaza.

President Biden and the leaders of the other mediating countries, Egypt and Qatar, said last week that they were prepared to present a “final” proposal to end the war, and they called on Israel and Hamas to return to the negotiating table after weeks of an impasse in talks.

In a joint statement, Mr. Biden, along with President Abdel Fattah el-Sisi of Egypt and Sheikh Tamim bin Hamad al-Thani of Qatar, declared that “the time has come” to conclude the deal for a cease-fire and the release of hostages abducted to Gaza in exchange for Palestinian prisoners and detainees held by Israel.

Israel will send its negotiating team to the meeting, which is expected to take place in Cairo or Doha, Qatar, “in order to finalize the details of the implementation of the framework agreement,” according to a statement from the office of Prime Minister Benjamin Netanyahu.

But with gaps on substantive issues remaining — and Mr. Netanyahu and Hamas officials trading blame for the failure to close them — there was little expectation that a deal could be concluded at Thursday’s meeting. It was unclear to what extent Hamas was willing to engage in the talks. In a statement on Sunday, the group said it objected to “more rounds of negotiations” and the introduction of any new proposals or conditions.

Major sticking points include Mr. Netanyahu’s demand for a mechanism to block armed militants from moving back into northern Gaza, though Israel left the wording vague and has not specified what kind of mechanism; and the lack of any agreement so far over which hostages and which Palestinian prisoners would be released in the first phase of the deal.

Against this backdrop, Israel was pressing ahead with its offensive in Gaza despite sharp international condemnation for a deadly strike on Saturday on a school compound where displaced Palestinians were sheltering.

The Israeli military issued a new evacuation order on Sunday for a neighborhood on the edge of a humanitarian zone, saying it was about to operate against armed groups in the area. It also said that its air force had struck about 30 Hamas targets throughout the Gaza Strip over the previous 24 hours, including military structures, an anti-tank missile launch post and weapons storage facilities.

Officials in Gaza said over the weekend that dozens of people had been killed in Israel’s strike on the school compound. The Israeli military disputed that account and defended the strike, saying it had carried out a precise operation and eliminated at least 19 militants who were using the compound as a command center.

The authorities in Gaza do not distinguish between combatants and civilians in reporting death tolls. In statements over the weekend, Hamas said that all those killed were civilians. None of the claims could be independently verified.

Israel’s political and military leaders have argued that it is essential to keep up the military pressure on Hamas, to force it to come to terms on a cease-fire deal.

Still, there was a sense of foreboding in Israel, which was preparing to observe the Jewish fast of Tisha B’Av, commemorating historic disasters that have befallen the Jewish people.

For the annual day of mourning, which starts at sunset on Monday and lasts through Tuesday, some rabbis have composed special prayers to mark the Hamas-led assault on southern Israel on Oct. 7, which prompted the war in Gaza.

The fast, traditionally marking the destruction of two ancient Jewish temples in Jerusalem, could also stoke tensions around a contested holy site in the city that is revered by Muslims as the Aqsa Mosque and by Jews as the site of the temples.

“When Gallant adopts the anti-Israel narrative, he harms the chances of reaching a hostage release deal,” the prime minister’s office said. “Israel has only one choice: To achieve total victory, which means eliminating Hamas’s military and governing capabilities, and releasing our hostages. This victory will be achieved.”

The rift comes during a critical week in the conflict, when Israel is bracing for an expected retaliation from Iran and its ally Hezbollah in Lebanon, even as intense diplomatic efforts are underway to hammer out a cease-fire in the Gaza conflict and avert a wider war.

For months, Mr. Netanyahu has said that he was committed to dismantling Hamas’s military and government, and to freeing Israeli hostages. But senior members of the Israeli security establishment have argued that the two goals can’t be achieved simultaneously. Some have argued that a cease-fire agreement with Hamas is the only way to bring the roughly 115 dead and living hostages home.

Hamas has consistently said any cease-fire agreement should include an end to the war and a full withdrawal of Israeli forces from Gaza. Mr. Netanyahu has suggested he would only be open to a temporary pause in the war of several weeks.

Mr. Gallant, a member of Mr. Netanyahu’s Likud party, has frequently been at odds with the prime minister, clashing with him over legislation seeking the overhaul of the Israeli judiciary, proposals for the future administration of Gaza, and the cease-fire talks.

After more centrist politicians left Mr. Netanyahu’s government in June, many political analysts said Mr. Gallant, who was a senior general in the military, became the main voice of moderation within the government’s decision-making circles.

General Ryder noted that Mr. Austin had already ordered additional combat aircraft and missile-shooting warships to the region. The orders came in response to threats from Iran and its proxies in Gaza, Lebanon and Yemen to attack Israel to avenge the assassination of a top Hamas leader, Ismail Haniyeh, in Tehran on July 31.

Mr. Austin has also directed the aircraft carrier Abraham Lincoln, equipped with F-35 fighter jets, to speed to the region, joining the aircraft carrier Theodore Roosevelt and its accompanying warships already in the Gulf of Oman.

A statement from the Israeli government said that Mr. Gallant had spoken to Mr. Austin about the Israeli military’s “readiness and capabilities in the face of threats posed by Iran and its regional proxies.”

The Israeli defense minister also discussed “the urgency of achieving an agreement for the release of hostages and thanked the U.S. administration for its leadership and commitment to this issue,” the statement said. The United States and Arab mediators are preparing to present what they have called a “final” proposal for a cease-fire in Gaza at a meeting on Thursday in the Middle East that Israel has said its negotiators will attend. Hamas has not indicated whether its representatives will be at the meeting.

The call between Mr. Austin and Mr. Gallant came a day after an Israeli airstrike hit a school compound in northern Gaza where displaced Palestinians were sheltering, an attack that Gazan authorities said killed dozens of people. Mr. Austin used the call to once again underscore the importance of “mitigating civilian harm” during Israeli operations in the enclave, General Ryder said.