WASHINGTON 

US President Joe Biden struck a hopeful note Friday as negotiators seeking to hammer out the details of a cease-fire to end the war in Gaza and free remaining hostages departed the Qatari capital of Doha before reconvening next week in Egypt.

"We are closer than we've ever been. I don't want to jinx anything," Biden told reporters in the Oval Office. "We may have something, but we're not there yet. It's much, much closer than it was three days ago. So keep your fingers crossed."

Earlier Friday, meditators from the US, Egypt and Qatar announced that they presented Israel and Hamas with what they called a "bridging proposal" to further narrow "remaining gaps in the manner that allows for a swift implementation of the deal."

A joint statement described the discussions, which transpired over two days, as “serious and constructive,” and said they “were conducted in a positive atmosphere.”

The mediators did not provide details of the new proposal but said that it is “consistent with the principles laid out by (US) President (Joe) Biden on May 31, 2024 and Security Council Resolution No. 2735.”

Their statement further noted that technical teams from Egypt, Qatar, and the US will “work over the coming days on the details of implementation, including arrangements to implement the agreement’s extensive humanitarian provisions, as well as specifics relating to hostages and detainees.”

It also mentioned that senior officials from the three countries will “reconvene in Cairo before the end of next week with the aim to conclude the deal under the terms put forward today.”

A senior Biden administration official, who briefed reporters on condition of anonymity, said mediators "aim to conclude this deal" during next week's meeting, describing the "bridging proposal" as essentially the same as what Biden laid out in May "with some clarifications based upon subsequent discussions and some of the details and implementation."

"This is a comprehensive arrangement. It has been negotiated for months, and we do believe very strongly that there's momentum here in this process," said the official.

A number of what are being called "working group engagements" will be carried out over the course of the next week to discuss outstanding issues, including the list of hostages and Palestinian prisoners that will be released, and the order by which they will be freed.

The official described the matter as "extremely complicated," saying it was "a large basis of the talks over the course of the last two days."

"There were some gaps there, and some trade space between the parties, which I think we've now gone a long way to bridge," the official added.

The negotiations involved CIA Director William Burns, Qatari Prime Minister Mohammed bin Abdulrahman Al Thani, Egyptian Intelligence Chief General Abbas Kamel, and Israeli Mossad Chief David Barnea.

Hamas has refused to participate in the discussions, demanding that Tel Aviv adhere to the agreements it made in July based on a proposal supported by US President Joe Biden two months prior, according to Israeli media.

More than 40,000 Palestinians have been killed during Israel's war in Gaza, the vast majority being women and children. Vast tracts of the coastal territory have been completely leveled amid relentless Israeli bombardment that has reduced entire neighborhoods to rubble.

Gazans continue to face acute shortages of food, water and medicine due to Israeli restrictions on the entry of humanitarian assistance, as well as the significant curtailment of movement for aid convoys once they enter the Strip.

A total of 1,139 people were killed in the cross-border attack led by Hamas on Oct. 7, which precipitated the current war.