Palestinian Authority President Mahmoud Abbas said Monday that he will formally apply for the UN membership on Friday, a UN spokesman told reporters.

Abbas, who is in New York at the UN Headquarters for the annual debate of the UN General Assembly, made the statement in his meeting with UN Secretary-General Ban Ki-moon, according to Ban's spokesman Martin Nesirky. "The secretary-general and President Mahmoud Abbas had a constructive meeting today," said Nesirky, adding that President Abbas had informed the secretary-general of his intention to submit on Friday an application for membership in the United Nations.

Last week, Ban told a press conference that he will pass the application to the Security Council if asked to do so by the Palestinians.

After that, the global peace and security body would examine it and come up with a resolution to recommend Palestinian statehood to the General Assembly. However, the U.S., a strong ally of Israel and one of the five permanent members of the 15-nation Council, is likely to use its veto power to thwart the Palestinians.

If the statehood bid in the Security Council fails, Abbas and the Palestinians could bring their case straight to the General Assembly, where it has widespread support. In this scenario, though, the Palestinians would only be able to gain non-member observer statehood. This would be a step up from their current status of permanent observer, but would not allow them to cast votes at the UN.

"The secretary-general reiterated his support for the two-state solution and 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, and discussed with President Abbas the ongoing Quartet efforts in this regard," Nesirky said, adding President Abbas had stressed his commitment to a "negotiated solution."

The Quartet, which groups the United States, the European Union, Russia and the United States, is a diplomatic group in search of the two-state solution -- an independent Palestine State to live in peace with a secure Israel.

Asked if the secretary-general had a preference concerning the Palestinian bid for UN membership, the spokesperson said this was a matter for member states to decide through the established procedures.

In response to a question on a meeting of the Quartet envoys, Nesirky said they held regular meetings and had met on Sunday in New York.