Abbas took the step in spite of pressure from the United States, The New York Times reported. Secretary-General Ban Ki-moon submitted Abbas' letter requesting membership to the Security Council, which is expected to discuss it next week.
Both Abbas and Israeli President Binyamin Netanyahu were scheduled to address the General Assembly Friday.
Earlier in the week Palestinian officials accused Washington of bullying several Security Council members into dropping their support for the Palestinian move, Palestinian officials said. Among the countries allegedly strong-armed were Portugal and Bosnia and Herzegovina, the officials told British newspaper The Guardian.
The United States allegedly threatened Portugal it would withhold support in financial institutions for its stricken economy and pressured Bosnia over its opposition to Balkan neighbor Kosovo's bid to be admitted to the United Nations, the officials said.
One senior Palestinian official told the newspaper the Obama administration was "playing a really nasty game," the newspaper said.
The State Department had no immediate comment.
On Wednesday, U.S. Secretary of State Hillary Clinton said Washington and Jerusalem were engaged in "extremely intense" diplomacy with council members. Washington has threatened to use its veto on the council.
Lebanon, which currently holds the rotating presidency of the Security Council, supports the Palestinian bid. Nine Security Council votes are needed for membership. Palestinian officials said they increasingly believed their request would fall short of the needed votes.
The vote would not come immediately in any case because the Security Council was expected to say it needed to review the request, which would allow time for diplomacy before the Palestinians move to their next option -- an approach to the General Assembly.
The broader body has the power to upgrade the Palestinian Authority to observer-state status, similar to that of the Vatican, but not to confer U.N. membership.
Adding a wrinkle to the Palestinian statehood bid, Iranian President Mahmoud Ahmadinejad said Thursday Tehran wouldn't recognize Israel's right to exist even if the United Nations did accept a Palestinian state. Ahmadinejad told reporters the Palestinian people should be allowed to hold a referendum on whether they wanted a two-state Israeli-Palestinian solution, as U.S. President Barack Obama and other Western leaders propose.