In a wide-ranging two-hour speech, Mr Abbas reiterated he would not accept the Trump administration as a mediator in peace talks with Israel and called for an internationally-led process.
He also accused Israel through its actions of ending the 1994 Oslo peace accords that form the basis of Palestinian ties with the Jewish state, saying the Palestinians would study all strategies for responding to it.
Beyond that, Mr Abbas attacked the US ambassadors to Israel and the United Nations, David Friedman and Nikki Haley, calling them a "disgrace".
Both Trump appointees have been strong supporters of Israel, with Mr Friedman having backed Jewish settlements in the West Bank.
"We said 'no' to Trump, 'we will not accept your project'," the Palestinian president said.
"The deal of the century is the slap of the century and we will not accept it," he added, referring to Mr Trump's pledge to reach the "ultimate deal" - Israeli-Palestinian peace.
The meeting in Ramallah of the Palestinian Central Council - a high-ranking arm of the Palestine Liberation Organisation - was called in the wake of Mr Trump’s December 6 recognition of Jerusalem as Israel’s capital.
The move has infuriated the Palestinians who want the annexed eastern sector of the city as the capital of their future state.
Prior to the declaration, Mr Trump and his envoys, including senior adviser and son-in-law Jared Kushner, had spent months seeking to negotiate how to restart talks between Israel and the Palestinians, stalled since 2014.
But since Mr Trump’s Jerusalem announcement, the Palestinians have refused to meet with the US administration, and Mr Abbas is expected to shun vice president Mike Pence when he visits the region next week.
US relations 'nadir'
In the buildup to the Central Council meeting on Sunday and Monday, Palestinian officials had stressed all options were on the table for responding to Mr Trump, including suspending the Palestine Liberation Organisation's recognition of Israel.
Mr Abbas did not mention recognition but said the Oslo accords that led to the creation of his Palestinian Authority and envisioned a final resolution to the conflict were in effect finished.
"I am saying that Oslo, there is no Oslo. Israel ended Oslo," he said, referring to persistent Israeli settlement building and other issues seen as eroding the possibility of a two-state solution to the conflict.
The 121-member council will meet Monday to discuss strategy for responding to Mr Trump's announcement, but Mr Abbas offered few concrete policy proposals.
Hugh Lovatt, Israel and Palestine Project Coordinator at the European Council for Foreign Relations, said while the speech was full of rhetoric, there was little noticeable policy.
"It is safe to say that president Abbas has done little to improve US-Palestinian relations which have now reached their nadir," he told AFP.
"Abbas's rambling speech was also noteworthy for what was not there - namely, any real vision for moving beyond the failed US-led Oslo paradigm.
"Those hoping for a glimpse of a new Palestinian strategy to end the occupation or a shift towards a one-state solution will have been left disappointed."
While Palestinian leaders have been outraged by Mr Trump's moves, they also face difficult choices in how to respond as they seek to salvage remaining hopes of a two-state solution to the conflict.
Earlier this month, Palestinian leaders said they will not be "blackmailed" after Mr Trump threatened to cut aid worth more than $300 million annually to force them to negotiate.
Mr Trump says "we refused negotiations. May God demolish your house. When did we refuse?", an indignant Mr Abbas asked.