Prime Minister Benjamin Netanyahu of Israel threw up a hurdle on Saturday to President Biden’s declaration a day earlier that it was “time for this war to end,” reiterating that Israel would not agree to a permanent cease-fire in Gaza before the destruction of Hamas’s military and governing capabilities.

President Biden, in an unusually detailed address at the White House on Friday, described what he said was a new Israeli proposal for a three-stage road map to a permanent cease-fire. But Israel remains deeply divided over the shape of any possible truce agreement — particularly whether to commit to an end to the war against Hamas.

As outlined by Mr. Biden, the proposal did not mention who would rule the Gaza Strip after the war. Unless other arrangements are reached, that could leave Hamas de facto in charge of the territory, which the Palestinian armed group would consider a major strategic victory after nearly eight months of an Israeli military offensive.

On Saturday, Mr. Netanyahu did not explicitly endorse or reject the proposal as outlined by Mr. Biden, which broadly conformed to previous Israeli truce plans. But the timing of his remarks, first thing the following morning, seemed to put the brakes on Mr. Biden’s hopes for a speedy resolution to the war.

“Israel’s conditions for ending the war have not changed: the destruction of Hamas’s military and governing capabilities, the freeing of all hostages and ensuring that Gaza no longer poses a threat to Israel,” Mr. Netanyahu’s office said in the statement released on Saturday morning.

Mr. Netanyahu has promised his public “absolute victory” against Hamas in Gaza, but its leaders have largely managed to evade Israeli attempts to take them out. He has pledged to bring home the remaining 125 living and dead hostages, but would most likely have to accede to Hamas’s demand for a permanent truce to do so. And if he did agree to such a deal, his far-right coalition allies could pull out, threatening his hold on power.

Analysts in Israel said Mr. Netanyahu’s carefully worded statement reflected those tensions after nearly eight months of war in Gaza. He has sought to buy time, balancing competing demands at home and abroad while avoiding tough decisions, they said.

Mr. Biden’s speech, however, may indicate that the clock is beginning to run out.

“Biden is challenging Israel, saying: ‘I am expecting you to allow this arrangement to go forward. Do not sabotage it. Do not drag the rug out from underneath it for political reasons,” said Uzi Arad, a former Israeli national security adviser under Mr. Netanyahu. “Put your money where your mouth is.”

But at home, Mr. Netanyahu faces a host of competing pressures.

President Biden outlined a cease-fire proposal at the White House on Friday.Credit…Cheriss May for The New York Times

The families of hostages held in Gaza have rallied public support for their call for a cease-fire deal amid rising fears over their loved ones’ fates, and large crowds regularly attend solidarity demonstrations in Tel Aviv. About 125 of the roughly 250 hostages taken captive by Hamas and other Palestinian militants are still in Gaza, and more than 30 of those are presumed dead, according to the Israeli authorities.

Gil Dickmann, whose cousin Carmel Gat was abducted from Kibbutz Be’eri during the Hamas-led massacre there on Oct. 7, conceded that the deal would be difficult to swallow for parts of the Israeli public. But he said reaching an agreement was critical, and not just for the remaining hostages.

“If this deal doesn’t go through, because of either Hamas or Israel, we are heading toward a forever war, where we sink deeper and deeper into the mud, dragging down Israelis, Palestinians, and certainly the hostages,” said Mr. Dickmann.

Some of Mr. Netanyahu’s far-right coalition allies have threatened to topple his government in the event of what they would view as a premature end to the war. And even moderate Israelis would likely wonder what the offensive in Gaza had really accomplished should a truce leave Hamas in power.

Mr. Netanyahu’s emergency unity government is already under threat: Benny Gantz, a rival who united with Mr. Netanyahu as a wartime measure, has threatened to leave unless the premier articulates a plan for postwar Gaza and to bring home hostages by Jun. 8. Mr. Gantz’s departure would not topple the government, but it would deprive Mr. Netanyahu’s hard-line coalition of its most moderate politicians, further straining its image abroad.

Yair Lapid, the leader of Israel’s parliamentary opposition, urged Mr. Netanyahu to take the deal as outlined by President Biden. He repeated that his party would back Mr. Netanyahu’s government if hard-liners like Itamar Ben Gvir, the national security minister, left over a hostage release deal.

Political analysts said Mr. Netanyahu has tried to avoid that scenario, as it would make him dependent on some of his harshest critics.

Israel and Hamas first observed a weeklong truce in late November during which 105 hostages and 240 Palestinian prisoners were released. Since then, both sides have dug in to seemingly intractable positions: Hamas conditioned any further hostage releases on Israel ending the war, while Israel vowed there would be no truce until it destroyed Hamas and brought home its hostages.