Addressing an emergency meeting of Muslim leaders in Turkey, Abbas said President Donald Trump was giving Jerusalem away as if it were an American city.
"Jerusalem is and always will be the capital of Palestine," he said, adding Trump's decision was "the greatest crime" and a violation of international law.
Wednesday's summit was hosted by Turkish President Tayyip Erdogan who has bitterly criticised the United States, a NATO ally, for its stance on Jerusalem.
"I invite all countries supporting international law to recognise Jerusalem as the occupied capital of Palestine. We cannot be late anymore," Erdogan told leaders and ministers from more than 50 Muslim countries.
He described Trump's decision last week as a reward for Israeli actions including occupation, settlement construction, land seizure and "disproportionate violence and murder".
"Israel is an occupying state (and) Israel is a terror state," he said.
Ahead of the meeting, Turkish Foreign Minister Mevlut Cavusoglu said Muslim nations should urge the world to recognise East Jerusalem as the capital of a Palestinian state within its pre-1967 borders.
He said this week Turkey was not seeking sanctions in response to the US move, but wanted the summit to issue a strong rejection of the US decision.
US 'bias'
The Trump administration says it remains committed to reaching peace between Israel and the Palestinians and its decision does not affect Jerusalem's future borders or status.
It says any credible future peace deal will place the Israeli capital in Jerusalem, and ditching old policies is needed to revive a peace process frozen since 2014.
Abbas told the leaders in Istanbul that Washington could no longer be an honest broker.
Israeli Prime Minister Benjamin Netanyahu has applauded Trump's declaration and said Washington had an irreplaceable part to play in the region.
"There is no substitute to the role that the United States plays in leading the peace process," he said at a Hanukkah holiday candle lighting ceremony on Tuesday.
Jordan is a US ally which signed a bilateral deal with Israel in 1994. Abdullah's Hashemite dynasty is also custodian of the Muslim holy sites in Jerusalem, making Amman sensitive to any changes in the city.
The summit was also attended by leaders including Iran's President Hassan Rouhani and Sudan's Omar al-Bashir. Rouhani tweeted that Trump's decision showed the United States had no respect for Palestinian rights and could never be an honest mediator.
The International Criminal Court has issued arrest warrants for Bashir over his alleged role in war crimes including genocide in Sudan's Darfur province, but Turkey is not a member of the court and not obliged to implement the warrants.