International mediators are making an urgent push for Israel and Hamas to reach a ceasefire and hostage deal next week after high-stakes negotiations in Qatar saw them put a fresh proposal to the warring parties.

The “bridging proposal” presented on Friday was intended to close the remaining gaps of disagreement between both sides, a joint statement from the US, Qatar and Egypt said.

US President Joe Biden expressed optimism about the state of ceasefire and hostage release talks that are expected to resume in Cairo next week. “We are closer than we’ve ever been,” he said, adding that the talks had brought the chances of a deal “much, much closer than it was three days ago.”

The two days of discussions took place amid tensions across the region about a potential Iranian attack against Israel, which carries the risk of scuppering already fragile negotiations.

The statement said the proposal “builds on the areas of agreement over the past week,” and “bridges remaining gaps in a manner that allows for a swift implementation of the deal.”

Senior officials from the US, Qatar and Egypt will meet again in Cairo before the end of next week, “with the aim to “conclude the deal under the terms put forward” Friday, the statement said.

The talks were “serious and constructive,” the statement added, though it did not elaborate on what points of agreement were achieved over the past week.

The death toll in Gaza since Israel launched its war against Hamas reached 40,000 people earlier this week, a bleak figure that underscores the desperation in the enclave for a reprieve from ten months of bloody conflict.

But discussions to bring about a pause have been shrouded in uncertainty since Israeli strikes in late July killed Hamas’ former political leader and senior figures in Lebanese militant group Hezbollah.

Hamas reiterated on Thursday its stance that there will be no hostage deal or ceasefire agreement without a complete withdrawal of Israeli troops from Gaza.

“Any agreement must achieve a comprehensive ceasefire, a complete withdrawal from Gaza, the return of displaced persons, reconstruction, in addition to a prisoner exchange deal,” Hussam Badran, a member of Hamas Political Bureau, said in a statement on Thursday.