NEW YORK, Sept 18 (Arshad Mohammed and Patrick Worsnip/Reuters) - A last-ditch international push began in New York on Sunday to try to relaunch Israeli-Palestinian peace talks and avert a crisis over Palestinian statehood at the United Nations.

Officials met two days after President Mahmoud Abbas said he would demand full membership of the world body for a Palestinian state at the U.N. General Assembly this week, setting up a diplomatic clash with Israel and the United States.

U.S. Secretary of State Hillary Clinton held talks with EU foreign policy chief Catherine Ashton on Ashton's recent trip to the region. We share the goal of trying to bring the parties back to the negotiating table, a U.S. official said.

Senior diplomats from the United States, Russia, the European Union and the United Nations -- the so-called Quartet of Middle East mediators -- also met on Sunday, an EU official said, as part of an intense effort in recent weeks to persuade the Palestinians to avoid a confrontation.

The official said the diplomats were assessing the situation, but gave no further details. They are likely to meet every day this week, a U.S. official said.

Washington and Israel say a U.N. vote over Palestinian statehood would damage chances for peace negotiations, arguing that a state can only be created through a settlement between the two sides.

But in a televised speech on Friday, Abbas said he would request the Palestinians' legitimate right, obtaining full membership for Palestine. The Palestinians say almost 20 years of on-off direct talks on statehood envisaged by interim peace accords have hit a dead end.

The United States says it will veto in the Security Council a Palestinian application for full U.N. membership, but former British Prime Minister Tony Blair, who serves an an envoy for the Quartet, said on Sunday a showdown could still be averted.

Blair told reporters, The Palestinians are here at the U.N. now, so the question is ... can people find a way that enables the Palestinians to take a significant step forward to statehood at the same time as not ending up in a situation where the U.N. replaces negotiations?

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The Quartet has for months been trying to put together guidelines for future peace talks, but so far without being able to agree on key details.

Blair told the ABC Television program This Week a proposed statement would set out where we want to go on issues like borders ... And I think what's going to be really important is also to give some sense of a timeframe, a timeline, if you like, for a successful negotiation.

The last round of the U.S.-backed talks between Abbas and Israeli Prime Minister Benjamin Netanyahu collapsed nearly a year ago. The Palestinians pulled out after Israel declined to extend a partial moratorium on settlement building in the West Bank on land the Palestinians want for their state.

Apart from borders, key points of contention include the status of Jerusalem, the future of Palestinian refugees and whether Israel should be acknowledged as a Jewish state.

The Palestinians say they will not resume talks unless the moratorium is reinstated. Israel says talks should resume without preconditions but that it accepts the idea that the Palestinians should ultimately have their own state.

Israeli Deputy Foreign Minister Danny Ayalon on Sunday told a Palestinian donors conference at the United Nations that Israel wanted to go on aiding Palestinian economic development, but that could change if the Palestinians declare a state.

Future assistance and cooperation could be severely and irreparably compromised if the Palestinian leadership continues on its path of essentially acting in contravention of all signed agreements, he said.

U.S. President Barack Obama is under pressure from Congress to back Israel's stance. Republican House speaker John Boehner told a Jewish group in Cincinnati on Sunday the U.S. commitment to Israel should be stronger than it's ever been.

Some in Congress have called for a suspension of U.S. aid to the Palestinians if they seek statehood. Donor aid is already declining but Sunday's U.N. conference called on donors to provide adequate and predictable funding. (Writing by Patrick Worsnip; Editing by Eric Walsh)