Washington (CNN) -- Envoys with the Mideast Quartet met again Tuesday after failing Monday to reach an agreement on how to jump-start stalled talks between Israelis and Palestinians.
After a two-and-a-half hour working dinner at the State Department Monday night, Secretary of State Hillary Rodham Clinton, U.N. Secretary-General Ban Ki-moon, E.U. foreign policy chief Catherine Ashton and Russian Foreign Minister Sergey Lavrov were unable to produce a unified statement on how to proceed.
"The major effort yesterday was to concert views on how best to encourage the parties back to the table," State Department spokeswoman Victoria Nuland told reporters Tuesday. "They're continuing to do that today. I'm not going to speak to, you know, the private diplomacy that went on in that room."
She added, "All the quartet can do, all any of us can do, is encourage them and nudge them back together. But it's the responsibility of the parties, the Israelis and the Palestinians, to get themselves to the table, to show the will to get to the table."
A senior administration official briefing reporters by telephone said the group had "substantive discussions" on Monday, but that there were "still gaps impeding progress" and that "much more work needs to be done" before the quartet can issue a call for the parties to re-launch negotiations.
The official spoke on condition of anonymity to discuss the sensitive diplomatic negotiations.
The official declined to give details on the "gaps."
Asked whether the push by the Palestinians to go to the United Nations in September in a bid to declare independence is creating a sense of urgency, the official said the Palestinians "are still evaluating" what they want in New York and still prefer negotiations as a way to reach independence.
Speaking Monday with reporters before the dinner, Secretary of State Hillary Clinton and E.U. foreign policy chief Catherine Ashton both said they remained committed to getting the two sides back to the table.
While violence in the region is down sharply from what it has been in recent decades, relations between Palestinian and Israeli leaders remain frosty with few formal talks about an "end-game" resolution to their long-running dispute.
"The work we're engaged in is trying to support both sides to get back into talks -- in a way, that will be the most important thing," Ashton added. "And perhaps there will be a time when ... a real celebration can begin."
The process got a jolt last month when Yasser Abed Rabbo, secretary-general of the Palestinian Liberation Organization's executive committee, which is led by President Mahmoud Abbas, read a statement announcing the government's intent to go to the United Nations in September and ask to be recognized as an independent country.
Its leaders hope to get "recognition for the country of Palestine within the 1967 borders ... on the basis of international legitimacy resolutions specific to Palestine since 1947," according to a report from the official WAFA news agency.
The Palestinian leadership added it is calling "on all (countries), without exception, to support this initiative" -- saying the move "will strengthen efforts to resume negotiations" over its relations with Israel.