Mr. Biden had anticipated that the plan would be unacceptable to some members of the Israeli government, Matthew Miller, a State Department spokesman, said on Monday.

“And of course, we’ve seen some members of the Israeli government already come out and oppose it,” Mr. Miller said. But he said that the proposal was “in the long-term security interests of Israel. It’s obviously in the long-term interests of the Palestinian people, as well.”

Mr. Miller said that since Mr. Biden announced the plan on Friday, Secretary of State Antony J. Blinken had spoken to the foreign ministers of Turkey, Qatar, Saudi Arabia, Jordan, Egypt and the United Arab Emirates. He had also spoken to Benny Gantz, a member of Israel’s war cabinet, and to Israel’s defense minister, Yoav Gallant.

“We’re completely confident,” that Israel supports the cease-fire plan, Mr. Miller said, adding that it was submitted last week to Hamas, which has yet to formally respond.

Hamas has said it “positively views” the proposal as described by Mr. Biden on Friday. It has not said whether it would accept the deal. On Sunday, Ghazi Hamad, a senior Hamas official, told an Egyptian news outlet that “the ball” was now “in the Israeli court.”

Mr. Netanyahu has insisted that the cease-fire proposal would enable Israel to continue fighting Hamas until all its war aims are achieved, including destroying the military and governing capabilities of the group, which led the deadly Oct. 7 attacks in southern Israel.

Two Israeli officials confirmed that the offer shared by Mr. Biden generally aligned with the most recent cease-fire proposal that Israel had presented in talks mediated by Qatar and Egypt.

As much as the world’s focus has been trained on the spiraling death toll and the humanitarian crisis in Gaza, in Israel the focus is on the safety and release of the hostages, many of them civilians, captured on Oct. 7 and taken to Gaza.