"If this LAST CHANCE agreement is not reached, all HELL, like no one has ever seen before, will break out against Hamas," Trump posted on his Truth Social platform.
The proposal, backed by Israeli Prime Minister Benjamin Netanyahu, calls for a ceasefire, the release of hostages within 72 hours, Hamas's disarmament and a gradual Israeli withdrawal from Gaza.
That would be followed by a post-war transitional authority headed by Trump himself.
"Hamas is still continuing consultations regarding Trump's plan... and has informed mediators that the consultations are ongoing and need some time," the official said on condition of anonymity because they were not authorised to speak publicly on the matter.
On Tuesday, Trump gave Hamas "three or four days" to accept his plan, which has been welcomed by world powers, including Arab and Muslim nations.
Mohammad Nazzal, a member of Hamas's political bureau, said in a statement Friday that the "plan has points of concern, and we will announce our position on it soon"