Top diplomats from the United States and Europe have begun a last-ditch international push to avert a looming showdown at the United Nations over Palestinian statehood that could crush already dim Mideast peace prospects.

U.S. Secretary of State Hillary Clinton and EU foreign policy chief Catherine Ashton held talks Sunday as part of an increasingly desperate effort to bring Israel and the Palestinians back to direct negotiations. Clinton said she and Ashton met to discuss “the way forward,” but she declined to reveal if mediators are making progress.

Senior envoys from the Mideast Quartet – the U.S., EU, U.N. and Russia – also met in New York Sunday.

Palestinian President Mahmoud Abbas has said he will seek full U.N. membership for an independent Palestinian state later this week – despite strong U.S. and Israeli opposition to unilateral moves on the statehood issue.

The U.S. says it will veto such an application in the Security Council. But former British Prime Minister Tony Blair – who serves as a Quartet envoy – said Sunday that a deal could still be reached.

Mr. Blair told ABC news that mediators will be looking for a way that allows Palestinians' “legitimate aspirations” to be recognized while renewing talks with Israel. He said direct Palestinian-Israeli negotiations are “the only thing that will produce a state.”

Mr. Abbas said in Ramallah Friday that U.N. membership is a legitimate right for Palestinian people. But, in talks with his Cabinet Sunday, Israeli Prime Minister Benjamin Netanyahu predicted the Palestinians' U.N. statehood bid will fail.

Even with a loss in the Security Council, the Palestinians are expected to take their case to the 193-member General Assembly, where a simple majority could grant a more symbolic recognition. The Palestinians currently hold observer status at the United Nations.

U.S.-mediated peace talks between Israel and the Palestinians stalled a year ago, after an Israeli moratorium on West Bank settlement construction expired. Palestinians oppose construction on land they want as part of a future state.

Mr. Abbas has said a Palestinian state must have the borders in place before Israel took control of the West Bank and Gaza Strip in the 1967 Arab-Israeli war.

American envoys have been shuttling between Israeli and Palestinian leaders in an attempt to revive direct talks and forestall the Palestinian statehood bid.

U.S. President Barack Obama is expected to meet with Mr. Netanyahu when both are at the U.N. General Assembly this week.