Abbas, who spoke at an extraordinary meeting of the Organization of Islamic Cooperation in Istanbul, did not elaborate on how the Palestinians intended to become a full member state.
Donald Trump's announcement has led to Palestinian protests in the occupied West Bank and Gaza strip. Clashes, Palestinian rocket fire and Israeli air strikes killed at least two people and left dozens of others wounded.
In the latest diplomatic fallout, the United States stood alone as, one after another, fellow UN Security Council members criticised Trump's decision in an emergency meeting of the world body.
(Reporting by John Davison and Nadine Awadalla, editing by Larry King)