Barack Obama has told the UN General Assembly the Palestinians deserve their own state, but that this would only be achieved through talks with Israel.
The US president's speech came as diplomatic efforts for Palestinian UN membership intensified, while thousands rallied in the West Bank.
He added there could be no "short cut" to peace, and is expected to urge the Palestinians to give up the initiative.
A Palestinian official said the UN would be given time to study the bid.
Mr Obama has held talks with Israeli Prime Minister Benjamin Netanyahu, and is to meet Palestinian leader Mahmoud Abbas later.
Mr Abbas has so far appeared determined to press ahead with the statehood bid on Friday, after his address to the UN General Assembly, with a written request to Secretary General Ban Ki-moon.
If his request is approved by Mr Ban, the Security Council will then examine and vote on it. In order to pass, the request must get the votes of nine out of 15 council members, with no vetoes from the permanent members.
The US has vowed to veto the request, and correspondents say Western diplomats are exploring ways to put off the voting process to buy themselves more time.
Should the Palestinian effort at the Security Council fail, Mr Abbas could ask for a vote of the General Assembly for enhanced observer status - which is enjoyed by others such as the Vatican - in which case no veto would be possible.
Speaking on the fringes of the summit, Palestinian negotiator Nabil Shaath said Mr Abbas would give "some time to the Security Council to consider first our full membership request before heading to the General Assembly".
French Foreign Minister Alain Juppe said later a UN vote on the issue was still "several weeks" away, suggesting there would be time to avoid a confrontation.
'Time has come'
Mr Obama earlier told the meeting: "Peace will not come through statements and resolutions at the UN."
"I am convinced that there is no short cut to the end of a conflict that has endured for decades."
"Ultimately, it is Israelis and Palestinians - not us - who must reach agreement on the issues that divide them: on borders and security; on refugees and Jerusalem."
After the US president's speech, French President Nicolas Sarkozy warned a veto of the Palestinian bid could spark another cylce of violence in the region. He suggested a compromise, saying the Israelis and Palestinians should be given a clear timeline - a month to start negotiations, six months to deal with borders and security and a year to finalise a "definitive agreement".
Analysts say this falls in line with an initiative previously promoted by EU foreign policy chief Catherine Ashton and the "quartet" of US, European, Russian and UN mediators.
The quartet's aim to give the two sides a year to reach a framework agreement is based on Mr Obama's vision of borders fashioned from Israel's pre-1967 boundary, with agreed land swaps.
UN Secretary General Ban Ki-moon opened the summit earlier with a call for new international efforts to break the Middle East stalemate.
He pledged "unrelenting" UN efforts to push forward the peace process.
Palestinians say their bid for statehood has been inspired by the Arab Spring, and is the result of years of failed peace talks.
In the West Bank on Wednesday, schools and government offices were shut to allow for demonstrations backing the UN membership bid in Ramallah, Bethlehem, Nablus and Hebron.
While UN recognition would have largely symbolic value, the Palestinians argue it would strengthen their hand in peace talks.
"The end of the Israeli occupation and a Palestinian state are the only path to peace," AFP quoted Mr Abbas' spokesman as saying after Mr Obama's speech.
"We will agree to return to the negotiations the minute that Israel agrees to end the settlements and the lines of 1967," added the spokesman, Nabil Abu Rudeina.
In his meeting with Mr Obama, Mr Netanyahu said direct negotiation was the only way to achieve a stable Middle East peace, adding that the Palestinian statehood effort was itself a short cut that "will not succeed".
The last round of talks broke down a year ago.
Efforts are now reportedly under way for the quartet to provide a basis for resumed peace negotiations, but work by mediators has yet to produce guidelines for the resumption of talks.
Both Mr Netanyahu and Mr Abbas have said they are prepared to engage in direct talks.