US President Donald Trump has urged everyone involved in efforts to end the Gaza war to "move fast" as mediators are set to meet in Egypt on Monday for indirect peace talks between Hamas and Israel, BBC reported.

The talks come after Hamas agreed to some parts of a 20-point US peace plan, including freeing hostages and handing over Gaza governance to Palestinian technocrats, but is seeking negotiations on other issues. 

The group's response did not mention the key demands of its disarmament and playing no future role in Gaza's governance, according to BBC.

Writing on social media that talks had been "very successful", Trump said: "I am told the first phase should be completed this week, and I am asking everyone to move fast."