Those pressures have led Israel to make significant concessions in the negotiations, two officials said, including an offer to release 15 Palestinians jailed on serious terrorism charges in exchange for five female Israeli soldiers being held in Gaza.

That offer was part of a broader proposal to exchange scores of Palestinian prisoners and detainees in exchange for about 35 other hostages during a roughly six-week cease-fire, the officials said.

Hamas’s political leaders have insisted, at least publicly, that any deal to release the more than 100 hostages still being held in Gaza is dependent on a permanent cease-fire and the withdrawal of Israeli troops. Israel has said it will not compromise on its goal of toppling Hamas in Gaza, suggesting it will not agree to a long-term truce.

At a news conference in Washington on Tuesday, Matthew Miller, a State Department spokesman, said that negotiators “made significant progress” last week and were continuing to push for an agreement between Israel and Hamas.

“We are trying to push this deal over the finish line,” Mr. Miller said. “We do think it’s possible.”

But he added, “Ultimately, some of this comes down to Hamas and whether Hamas is willing to agree to a deal that would provide significant benefits to the Palestinian people that they claim to represent.”

With no accord in place, the Palestine Red Crescent Society said it had suspended emergency medical missions for two days in a part of Gaza where Israeli forces on Sunday intercepted a convoy evacuating patients from a hospital, interrogating and detaining workers on the suspicion that they were ferrying Hamas fighters.

The Red Crescent and U.N. officials said they had cleared arrangements for the evacuation with the Israeli authorities. Jens Laerke, a spokesman for the U.N. aid office in Geneva, said on Tuesday that Israel had known the details of the route, the vehicles and the identities of those traveling in the convoy.

But after the convoy left Al-Amal Hospital in the southern city of Khan Younis, carrying 24 patients who required surgery, it was stopped by Israeli forces.

The soldiers ordered patients and aid workers out of the vehicles, forced paramedics to strip and held the convoy for seven hours, U.N. officials said. One of those detained was released hours later, the Red Crescent said.