Secretary of State Antony J. Blinken pressed on Tuesday for a cease-fire in the Gaza Strip, but officials familiar with the latest U.S.-backed proposal said it left major disagreements between Hamas and Israel unresolved.

After meeting with Prime Minister Benjamin Netanyahu of Israel on Monday, Mr. Blinken said that Israel had accepted the U.S. proposal — the details of which have not been made public — and that the onus was now on Hamas to agree to it as well. But Israeli and Hamas officials have downplayed the idea that a deal could be imminent, saying that mediators’ efforts — and the latest American proposal aimed at bridging gaps between the two sides — have failed to resolve some of the most substantive disputes in the talks.

Mediators have previously called for high-level talks to resume in Cairo this week. A senior Biden administration official said on Tuesday night that he expected negotiations to continue this week, but declined to say when. Two Israeli officials said it was unclear where and when they would next convene.

President Biden, who remarked briefly on the negotiations after his speech at the Democratic National Convention in Chicago on Monday night, drew a critical response from Hamas after he said the group was “now backing away” from a cease-fire deal.

On Tuesday, as Mr. Blinken traveled to Egypt and Qatar to push for an agreement, Hamas said it was eager to reach a cease-fire but that the latest American proposal was “a reversal” from what it had agreed to in early July. Hamas accused the United States of bowing to what it called “new conditions” from Israel.

Before boarding his return flight to the United States, Mr. Blinken told reporters: “This needs to get done. And it needs to get done in the days ahead and we will do everything possible to get it across the finish line.”