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His comments came after a UN General Assembly vote effectively repudiated Washington's controversial declaration.
A majority of countries backed a non-binding resolution affirming Jerusalem's status quo on Thursday, the BBC reported.
In a Christmas message, Abbas said that the US has chosen to be biased and pick Israel's side, ignoring international law and UN resolutions.
"It is because of this US decision to support illegality and the blatant violations of our rights that we will not accept the US as the mediator in the peace process nor are we going to accept any plan from the US side," Abbas said in the message.
He also rebuffed a new US framework for peace being developed by President Donald Trump's Middle East envoy, Jared Kushner, before it has been launched.
He stated that Trump's decision was "an insult to millions of people" and has also been rejected by local Christian churches.
"This time every year, the souls of billions of people turn to Bethlehem to celebrate the birth of Jesus Christ, the messenger of love, peace and justice," Abbas said.
"Bethlehem, the birthplace of hope, continues to be affected by the Israeli plans to create 'Greater Jerusalem' on the suffering of Palestinians," he added.
As protests continued, a 24-year-old Palestinian in northern Gaza was killed in clashes with Israeli troops, the Palestinian Health Ministry said. Israel said it was looking into the report.
There were also violent confrontations between demonstrators and troops across the occupied West Bank for the third straight Friday, including in Bethlehem.