Abbas and Ban also discussed international efforts to avoid a showdown over the bid in a meeting hours after the Palestinian leader`s arrival in New York on Monday to make the bid for UN recognition of a Palestinian state.
The United States has vowed to veto any application to the UN Security Council which must support any membership.
"President Abbas informed the secretary general of his intention to submit to the secretary general on Friday an application for membership in the United Nations," said UN spokesman Martin Nesirky.
"The secretary general informed president Abbas of his intention to perform his duties under the UN Charter."
In response, Ban "stressed his desire to ensure that the international community and the two parties can find a way forward for resuming negotiations within a legitimate and balanced framework," Nesirky told reporters.
Ban "discussed with president Abbas the ongoing Quartet efforts in this regard," the UN spokesman said, referring to the diplomatic Quartet on the Middle East comprised of the United States, Russia, the European Union and the United Nations.
"President Abbas stressed his commitment to a negotiated solution," he said.
The 15-member Security Council must support any Palestinian bid for full membership of the UN. But the UN General Assembly could decide alone to give enhanced observer member status and no veto is possible. (*)
Editor: Kunto Wibisono
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