|Hillary Clinton hosted a dinner for the Quartet, which is likely to be the group's last before September [AFP]
Mahmoud Abbas, the Palestinian president, has vowed to pursue the bid for statehood at the UN General Assembly in New York in September.
The announcement comes after mediators of the Middle East Quartet failed to announce any progress in their meeting in Washington on Monday about how to revive stalled Israeli-Palestinian peace talks.
Abbas called the Mideast Quartet's silence "a negative indication" of "deep division between them".
"We will go to the United Nations and we hope the US wilil not use its veto, but that we will go with its agreement," Abbas said, after a meeting on Tuesday in Athens with Karolos Papoulias, the Greek president.
The Palestinian UN bid is for statehood on the lines that existed before the 1967 War, covering the Gaza Strip and the West Bank, including East Jerusalem.
Israel, the US and some European governments oppose the plan and the Quartet had been expected to draw up a new initiative for peace talks that could persuade the Palestinians to drop the bid.
Saeb Erekat, a Palestinian negotiator, told the AFP news agency that "there is no other option but to support the Palestinian plan" to seek statehood.
"It is time for the international community to support the Palestinian plan to obtain membership for the state of Palestine on the 1967 borders because this approach will preserve the peace process and the two-state solution," Erekat said.
Peace talks between the Palestinian and Israeli sides have been in stalemate since September 2010, when Israel refused to renew a partial Israeli settlement freeze that had expired.
Palestinians say they will not engage in dialogue amid Israeli construction on land they want for a future state.
Monday's dinner was likely to be the last meeting of the peacemaking group before the Palestinians seek full UN membership when the General Assembly convenes in September.
The Quartet representatives - Ban Ki-moon, the UN chief; Catherine Ashton, the EU foreign policy chief; Tony Blair, the former British prime minister and Quartet envoy; Hillary Clinton, the US secretary of state; and Sergei Lavrov, the Russian foreign minister - did not issue a public statement about their working dinner on Monday.
Without a statement and action plan, Monday's talks suggested that the parties were unable to agree on the best way forward.
Haaretz, an Israeli daily newspaper, reported on Tuesday that the issue of recognising Israel as a Jewish state was responsible for the Quartet failing to reach an agreement.
The report cited an unnamed Western diplomat who said: "The goal was to give each side something that was important to them".
"The Palestinians were supposed to get 1967 borders with land swaps and the Israelis wanted to receive in return the recognition of Israel as the Jewish homeland, but there was no agreement on this matter," the diplomat said.
Israeli officials had no immediate comment on Monday's meeting.
A senior official in US President Barack Obama's administration spoke of "gaps" which are "impeding progress", without elaborating on the nature of the differences.
"More work needs to be done to close those gaps," the official said after the meeting, on condition of anonymity.
He said that the parties perceived "an urgent need" to "find a way to resume direct negotiations without delay or preconditions", and need to do more work "privately, quietly" to see if the gaps cannot be closed.
"There is a time and a place for public statements and there is a time and a place for private diplomacy," he said.
However, Sergei Lavrov, the Russian foreign minister, called the dinner "a good meeting", rebuffing suggestions of rift among the Quartet members.
"The fact that we didn't produce a statement doesn't mean we disagree and abandoned the effort," Lavrov said on Tuesday in Washington. "Our experts continue to discuss it."