Prime Minister Benjamin Netanyahu of Israel maneuvered into rougher political waters on Monday, as two far-right partners threatened to bring down his government should Israel agree to a cease-fire deal that would end the war in Gaza without eliminating Hamas.

Mr. Netanyahu told lawmakers in a closed-door meeting on Monday that President Biden had not presented the “whole picture” when he described a proposed cease-fire from the White House last week, according to a person who attended the meeting and requested anonymity.

Mr. Netanyahu, however, expressed openness to a 42-day pause in the fighting, the person said, embracing at least part of the first phase of the three-part cease-fire plan.

Mr. Biden called the three-phase proposal, which he said was put forward by Israel, a road map to an “enduring cease-fire” and to the release of the remaining hostages in Gaza. If Hamas abided by the agreement’s terms, the president said, it would ultimately lead to the “cessation of hostilities permanently.”

“It’s time to end this war,” Mr. Biden said

Two-far-right members of Mr. Netanyahu’s governing coalition, Itamar Ben-Gvir, the national security minister, and Bezalel Smotrich, the finance minister, said on Monday that they could not accept any deal that stops short of completely eliminating Hamas.

As Mr. Biden described it on Friday, the Israeli military’s attacks in Gaza had already eliminated Hamas as a major threat, and that “at this point, Hamas is no longer capable of carrying out another Oct. 7.”