Waving a copy of the request before the UN General Assembly to huge applause, Abbas said he had submitted an "application for the admission of Palestine on the basis of the June 4, 1967 borders," with Jerusalem as its capital.
He also called for Secretary General Ban Ki-moon "to expedite transmittal of our request to the Security Council and I call upon the distinguished members of the Security Council to vote in favor of our full membership."
"Here I declare that the Palestine Liberation Organization is ready to return immediately to the negotiating table on the basis of the adopted terms of reference... and a complete cessation of settlement activities," Abbas told the UN General Assembly.
But he maintained previous peace talks were "smashed against the rocks of the positions of the Israeli government, which quickly dashed the hopes raised by the launch of negotiations last September."
The Palestinian leader won huge applause and a standing ovation Friday from some of the assembly as he entered the hall shortly after asking the UN to admit the state of Palestine.
There was also applause when he paid tribute to the late Palestinian leader Yasser Arafat, during his speech to the annual assembly meeting.
And he sought to reassure the Israelis: "Our efforts are not aimed at isolating Israel or delegitimizing it; rather we want to gain legitimacy for the cause of the people of Palestine."
"We only aim to delegitimize the settlement activities, the occupation and apartheid and the logic of ruthless force, and we believe that all the countries of the world stand with us in this regard."