Mr Trump’s deal, which proposes an independent Palestinian state, includes US recognition of Israeli annexation of settlements in the occupied West Bank.
Israeli officials are yet to comment on the announcement.
PA security forces and Israel have previously maintained cooperation in policing areas of the occupied West Bank that are under Palestinian control.
It has also held agreements with CIA in terms of sharing intelligence despite Palestinian efforts to boycott Trump’s peace in 2017.
Mr Abbas said he had rejected offers from Mr Trump to discuss his plan over the phone or receive a copy of it.
He said: “Trump asked that I speak to him by phone but I said ‘no’, and that he wants to send me a letter … but I refused it.
“I will not have it recorded in my history that I sold Jerusalem.”
The Arab League also rejected the US President’s plan, calling it “unfair” to Palestinians.
In a statement the pan-Arab bloc said that the deal “does not meet the minimum rights and aspirations of Palestinian people.”
The League said it would not cooperate with the US in implementing it.
