UNITED NATIONS — The Palestinian president, Mahmoud Abbas, said Monday that he would present an application for Palestine to join the United Nations immediately after he addresses the General Assembly on Friday, as diplomats worked frenetically to try to limit the fallout from the application.

Mr. Abbas told Ban Ki-Moon, the United Nations secretary general, that he was determined to move forward.

“I think it has dawned on everybody that they cannot convince us not to go,” said Hanan Ashrawi, a member of the Palestinian delegation. “Most people are discussing what is next.”

Envoys from the Quartet — the grouping of the United States, Russia, Europe and the United Nations established in 2002 to help guide the Israeli-Palestinian negotiations — were trying to overcome substantial recent differences to present a united draft statement that might lead quickly to direct negotiations between the two parties.