DOHA/CAIRO, Jan 14 (Reuters) - Negotiators will meet in Doha on Tuesday seeking to finalise details of a plan to end the war in Gaza after U.S. President Joe Biden said a ceasefire and hostage release deal he has championed was on “the brink” of coming to fruition.

Mediators gave Israel and Hamas a final draft of an agreement on Monday, an official briefed on the negotiations said, after a midnight “breakthrough” in talks attended by envoys of both the outgoing U.S. president and President-elect Donald Trump.

“The deal … would free the hostages, halt the fighting, provide security to Israel and allow us to significantly surge humanitarian assistance to the Palestinians who suffered terribly in this war that Hamas started,” Biden said in a speech on Monday to highlight his foreign policy achievements.

If successful, the ceasefire deal would cap over a year of start-and-stop talks and lead to the biggest release of Israeli hostages since the early days of the conflict, when Hamas freed about half of its prisoners in exchange for 240 Palestinian detainees held by Israel.

The official briefed on the talks, who did not want to be identified, said the text for a ceasefire and release of hostages was presented by Qatar to both sides at talks in Doha.

“I think there is a good chance we can close this … the parties are right on the cusp of being able to close this deal,” Biden’s national security adviser Jake Sullivan told reporters on Monday. U.S. Secretary of State Antony Blinken said the ball was in Hamas’ court. Hamas said it was keen to reach a deal.