After more than 15 months of nearly uninterrupted fighting in Gaza, diplomats trying to broker a cease-fire between Israel and Hamas expressed cautious hope on Tuesday that a deal could finally be within reach.

But that optimism was tempered — by the uncertainty of whether both sides would ultimately agree, by what details could still change and by the experience of months past in which cease-fire talks repeatedly collapsed.

“We believe that we are at the final stages, but until we have an announcement — there will be no announcement,” Majed al-Ansari, the foreign ministry spokesman for one of the mediating countries, Qatar, told reporters on Tuesday.

Here’s what we know about the potential cease-fire agreement.

What is the state of the talks?

The U.S. secretary of state, Antony J. Blinken, said on Tuesday that Israel and Hamas were “right on the brink” of agreeing to a deal to pause the fighting in Gaza and release hostages held there in exchange for Palestinians held in Israeli jails.

He and diplomats from other mediating countries, including Qatar and Egypt, have for months failed to reach a breakthrough in talks, but they have made progress quickly in recent weeks.

Mediators “managed to minimize a lot of the disagreements between both parties,” Mr. al-Ansari said, adding that they were focused on “the final details of reaching an agreement.”