Speaking at a press conference in the West Bank city of Ramallah, Abbas said the Palestinians remain committed to ending the Israeli occupation and establishing a state with its capital in east Jerusalem.
"After the nonsense that we heard today we say a thousand noes to the Deal of The Century," he said. "We will not kneel and we will not surrender.”
The Middle East peace plan proposes a Palestinian state in parts of the West Bank but would allow Israel to annex its settlements in the occupied territory. The plan would allow the Palestinians to establish a capital on the outskirts of East Jerusalem but would leave most of the city under Israeli control.
“This is what a future State of Palestine can look like, with a capital in parts of East Jerusalem,” Trump tweeted, following his announcement alongside Israeli Prime Minister Benjamin Netanyahu.
Protests meanwhile broke out across the Gaza Strip, an area controlled by the Islamic militant group Hamas. Protesters burned tires and pictures of Trump and Netanyahu.
Later Tuesday, Palestinian protesters clashed with Israeli forces on the outskirts of Ramallah, near the Jewish settlement of Beit El.
Abbas held an emergency meeting with other Palestinian factions to discuss a unified response to the Middle East peace plan. Abbas had rejected the deal before it was announced saying the U.S. was favoring Israel.
EU foreign policy chief Josep Borrell said Trump's initiative "provides an occasion to re-launch the urgently needed efforts towards a negotiated and viable solution" to the conflict.
He reiterated the bloc's commitment to a "negotiated and viable two-state solution that takes into account the legitimate aspirations of both the Palestinians and the Israelis, respecting all relevant U.N. resolutions and internationally agreed parameters."
Jordan and Egypt, the only two Arab countries to have made peace with Israel, urged for measured responses from both sides.
Jordan warned against any Israeli "annexation of Palestinian lands" and reaffirmed its commitment to the creation of a Palestinian state based on borders before the 1967 Arab-Israeli War.
Egypt urged Israelis and Palestinians to "carefully study" the plan and said it appreciates the administration's efforts.
The Egyptian Foreign Ministry said in a statement Tuesday that it favors a solution that restores all the "legitimate rights" of the Palestinian people through establishing an "independent and sovereign state on the occupied Palestinian territories."
Fox News' Andrew O'Reilly and The Associated Press contributed to this report.