"The United States has proven to be a dishonest mediator in the peace process and we will no longer accept any plan from the United States," Abbas said after meeting French President Emmanuel Macron in Paris.
He also hit out at efforts by the US to intimidate countries ahead of a vote at the UN on Thursday which saw 128 countries condemn Washington's decision on 6 December to recognise Jerusalem as the Israeli capital.
"I hope that the others will learn the lesson and understand that you cannot impose solutions by using money and trying to buy off countries," he added.
Macron repeated his earlier condemnations of the US decision on Jerusalem, but he also ruled out recognising Palestine as a state unilaterally which France has mooted previously.
"The Americans have marginalised themselves and I am trying to not do the same thing," Macron told the joint press conference with Abbas.
He added: "The solution will be built around two states so inevitably there will be a moment in the process when there is recognition. I want to do it at a moment that will help build peace on the ground."
Macron has also ruled out launching a fresh French peace initiative in the short term, saying he is waiting to see what happens with the American effort which Abbas rejected on Friday.
The 40-year-old French leader has stepped up his meetings with leaders from the Middle East in recent weeks, hosting Israeli President Benjamin Netanyahu in Paris less than a fortnight ago.
Jordanian King Abdullah II visited on Thursday, the day before Abbas' arrival.
Macron said he would visit the Palestinian territories in 2018.
"I have committed myself very clearly to doing everything" to further the peace process, Macron said.
Abbas praised Macron's efforts as a mediator.
"We have trust in you. We respect the efforts made by you and we count heavily on your efforts," he said.