The 20-point plan includes an end to fighting, the return of Israeli hostages and an international "Board of Peace" to help run Gaza, which would include former UK Prime Minister Tony Blair.
Trump - who announced the plan alongside Israeli PM Benjamin Netanyahu - says if Hamas doesn't accept, he gives Israel "full backing to do what you would have to do".
Meanwhile, Israel continues its offensive in Gaza, saying its air force hit 160 targets across the Strip on Monday.
