US President Joe Biden said on Monday that a ceasefire and hostage-release deal between Hamas and Israel is "on the brink" of being finalised, amid growing optimism in Washington about negotiations in the Middle East.

"In the war between Israel and Hamas, we're on the brink of a proposal that I laid out in detail months ago finally coming to fruition," Biden said in a farewell speech at the State Department.

Biden has been working the phones as he seeks a prized peace deal in his final days in office before Donald Trump returns to the White House on January 20.

He said the proposed agreement would include a surge of aid to Palestinians in Gaza, the release of hostages held by Hamas and a halt to the fighting in the enclave.

"We're working urgently to close this deal," Biden said.

The outgoing US president said he would be speaking soon to Egypt's President Abdel Fattah al-Sisi, who has played a key role in negotiations.

He also spoke to Israeli Prime Minister Benjamin Netanyahu on Sunday and called the ruler of mediator Qatar, Sheikh Tamim bin Hamad Al-Thani, on Monday.

A peace deal has seemed within reach on a number of previous occasions since the Gaza war broke out following Hamas's October 6, 2023 attack on Israel, only then to collapse.

But optimism is growing in Washington that an agreement is possible.

US National Security Advisor Jake Sullivan said earlier Monday as that a truce was "close."

"We are close to a deal, and it can get done this week," Sullivan told reporters at the White House.

"I'm not making a promise or prediction, but it is there for the taking, and we are going to work to make it happen."

Sullivan said the "gaps have fundamentally narrowed down" between Israel and Hamas. (AFP)