Biden said on Friday that Israel had offered a new roadmap towards a full ceasefire that would see Israeli forces withdraw from all populated areas of Gaza and the release of captives held by Palestinian group Hamas
But Netanyahu's far-right coalition partners National Security Minister Itamar Ben Gvir and Finance Minister Bezalel Smotrich said they would quit his government if the deal went ahead.
Ben Gvir said his party would "dissolve the government" while Smotrich said he would "not be part of a government that will agree to the proposed outline".
"Agreeing to such a deal is not total victory -- but total defeat," Ben Gvir said on social media platform X.
"We demand the continuation of the war until Hamas is destroyed and all hostages return," Smotrich said in a separate post.
Earlier on Saturday, Netanyahu insisted that the destruction of Hamas was part of the Israeli plan laid out by Biden.
Israeli opposition leader Yair Lapid vowed to offer Netanyahu "our safety net for a hostage deal if Ben Gvir and Smotrich leave the government".
Without Ben Gvir's and Smotrich's parties, Netanyahu's coalition could lose its majority in parliament.
Thousands of Israelis meanwhile rallied in Tel Aviv to demand acceptance of the ceasefire and captive release deal outlined by Biden, with many fearing the premier would disown the proposal.
"I hope that somehow Biden puts enough pressure so the government and Netanyahu will take the deal," protester Diti Kapuano, 46, told AFP.
Israel says 121 captives are still being held in Gaza, including 37 the army says are dead.
Israel's war on Gaza has killed at least 36,379 Palestinians and wounded more than 80,000, mostly women and children, according to Gaza health officials.
The bloodiest Gaza war erupted on October 7 after Hamas launched a surprise offensive into southern Israel.
The ensuing chaos and a frantic Israeli defence response led to 1,189 deaths, according to an AFP tally of Israeli official figures.
*This story was edited by Ahram Online
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