Secretary of State Antony J. Blinken said on Monday that Israel had accepted a Biden administration proposal to bridge some remaining differences with Hamas on a cease-fire deal, as he pushed what he called “probably the best, maybe the last, opportunity” to secure a truce and free the remaining hostages in Gaza.

Mr. Blinken made the declaration after a nearly three-hour meeting with the Israeli prime minister, Benjamin Netanyahu, in Jerusalem. “In a very constructive meeting with Prime Minister Netanyahu today, he confirmed to me that Israel accepts the bridging proposal — that he supports it,” Mr. Blinken told reporters. “It’s now incumbent on Hamas to do the same.”

The statement put new pressure on Hamas, whose officials have called the proposal fundamentally slanted toward Israel, although the details have not been publicized.

Osama Hamdan, a Hamas official, said in a televised interview on Monday with Al Jazeera that Hamas had broadly accepted a framework for a cease-fire outlined by President Biden in late May. But he accused Mr. Netanyahu of introducing new conditions to that proposal and said Israeli officials had conceded nothing on key issues during a round of talks in Doha, Qatar, last week.

“If the U.S. administration was serious, we wouldn’t need more negotiations — only to implement Biden’s proposal,” Mr. Hamdan said.

Mr. Netanyahu’s office said in a statement that the meeting with Mr. Blinken had been “positive” and that the prime minister had “reiterated Israel’s commitment to the current American proposal on the release of our hostages, which takes into account Israel’s security needs, which he strongly insists on.”