Netanyahu may be forced to choose between a cease-fire and his government’s survival.

For months, Prime Minister Benjamin Netanyahu of Israel has refused to offer a timeline for ending the war against Hamas in Gaza, a reticence that his critics see as a political tactic. But he has been put on the spot this weekend by President Biden’s announcement outlining a proposal for a truce.

Mr. Netanyahu, a conservative, has long juggled competing personal, political and national interests. He now appears to be facing a stark choice between the survival of his hard-line, hawkish government and bringing home hostages held in Gaza while setting himself and Israel on a new course away from growing international isolation.

Critics of the prime minister have portrayed him as indecisive and say there are two Netanyahus: one who functions pragmatically in the small war cabinet he formed with some centrist rivals, boosting its public legitimacy; and another who is effectively being held hostage himself by the far-right members of his governing coalition, who oppose any concession to Hamas and who ensure his political survival.

Mr. Biden on Friday outlined broad terms that he said were presented by Israel to the American, Qatari and Egyptian mediators who have been pushing for a deal to pause the fighting and free hostages held in Gaza. Israeli officials confirmed that the terms matched a cease-fire proposal that had been greenlit by Israel’s war cabinet but not yet presented to the Israeli public.

Now, analysts say, it is crunchtime for Mr. Netanyahu, or Bibi, as he is popularly known.

Mr. Biden “booted Netanyahu out of the closet of ambiguity and presented Netanyahu’s proposal himself,” Ben Caspit, a biographer and longtime critic of Mr. Netanyahu, wrote in Sunday’s Maariv, a Hebrew daily. “Then he asked a simple question: Does Bibi support Netanyahu’s proposal? Yes or no. No nonsense and hot air.”

The leaders of two far-right parties in the coalition — Bezalel Smotrich, Israel’s minister of finance, and Itamar Ben-Gvir, the national security minister — have explicitly threatened to bring Mr. Netanyahu’s government down if the prime minister goes along with the deal outlined by Mr. Biden before Hamas is fully destroyed. Some hard-line members of Mr. Netanyahu’s own Likud party have said they will join them.

At the same time, Benny Gantz and Gadi Eisenkot, two former military chiefs who joined the emergency government for the duration of the war, have threatened to withdraw the support of their centrist National Unity party by June 8 if Mr. Netanyahu fails to come up with a clear path forward. And opposition parties have begun organizing to try to topple the government.

The cease-fire proposal involves three phases. They would see tranches of hostages released in exchange for hundreds of Palestinian prisoners in Israeli jails; a temporary cease-fire would turn into a permanent cessation of hostilities, with the third phase involving an internationally backed effort to rehabilitate Gaza.

More than 100 hostages were released under a more limited deal last November. An estimated 125 hostages, living and dead, are still held by Hamas and other armed groups in Gaza.

Ophir Falk, the chief foreign policy adviser to Mr. Netanyahu, said in an interview with Britain’s Sunday Times that Mr. Biden’s proposal was “a deal we agreed to.” Adding that many details still had to be worked out, Mr. Falk said, “It’s not a good deal but we dearly want the hostages released, all of them.”

Israelis were left to parse the two statements following Mr. Biden’s speech that Mr. Netanyahu’s office put out, unusually, during the Sabbath. The statements neither forcefully endorsed the proposal nor denied that it had been presented to the mediators. Instead, they were conditional and open to interpretation — seemingly designed to leave Mr. Netanyahu’s options open.

The first statement said that Mr. Netanyahu had authorized Israel’s negotiating team to present a proposal that would see the release of the hostages and also “enable Israel to continue the war until all its objectives are achieved, including the destruction of Hamas’s military and governing capabilities.”

The second reiterated those conditions for ending the war and added, “The notion that Israel will agree to a permanent cease-fire before these conditions are fulfilled is a non-starter.”

Notably absent, though, was Mr. Netanyahu’s oft-stated goal of “total victory” over Hamas in Gaza — a slogan that Mr. Biden on Friday dismissed as a vague objective that would mean indefinite war.