The meeting at the Egyptian Red Sea resort comes a year after peace talks were relaunched in Annapolis in the US, but there is little sign that the ambition of reaching a deal by the end of the year can be achieved.
Political turmoil in Israel which has led to early elections being called, and a lingering feud between rival Palestinian factions have hampered efforts to seal a deal.
Ban Ki-moon, the UN secretary-general, reading from the Quartet's final statement, said: "The Quartet called for the continuing of the peace process in the framework of Annapolis.
"Without minimising the gaps and obstacles that remain, the representatives of the parties shared their assessment that the present negotiations are substantial and promising."
The statement also criticised "terrorism" and the building of illegal settlements by Israel.
Leadership 'vacuum'
Tony Blair, the Quartet's special Middle East envoy and former UK prime minister, gave Al Jazeera an upbeat assessment of the talks saying that progress had been made, even if there was "still a long way to go".
While acknowledging that a political leadership "vacuum", as Barak Obama waits to assume the US presidency and Israel prepares for elections, could be a set-back to negotiations, he urged the rest of the international community to "come together on the critical elements of the deal" and "show drive and commitment to get it done".
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"Unfortunately, the Quartet will not declare what it should have declared, and that's the failure of Annapolis"
Mustafa Barghouthi, Palestinian MP
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However, Mustafa Barghouthi, a Palestinian MP and president of the Palestinian national unity initiative, said the group was no closer to achieving a breakthrough.
He told Al Jazeera: "I think, unfortunately, the Quartet will not declare what it should have declared, and that's the failure of Annapolis.
"For a whole year, the Palestinians have been given promises on paper, while they have seen on the ground the building blocks of an Israeli apartheid system."
Barghouthi said the election of Obama as US president could push the two sides closer to a settlement, but only if the president-elect met three key challenges.
Firstly, to "neutralise the Israeli" policy influence in the US, secondly, to "take a more balanced position" on the conflict and, finally, "to see the reality that... Israel has created a system of apartheid".
George Bush, the outgoing US president, had hoped to achieve a deal before he leaves office in January, but Condoleezza Rice, the secretary of state, has admitted that there is no breakthrough in sight.
"The distance to peace has been narrowed although peace has not been achieved," Rice said after meeting Mahmoud Abbas, the Palestinian president, on Friday.
In the absence of a full accord, Rice is pushing the two sides to define the outlines of a deal before she hands over to the Obama administration in January.
"One of the things we must do is that we must show ... that Annapolis has laid the foundation for the establishment of the state of Palestine," she said.
Abbas and Tzipi Livni, the head of Israel's ruling Kadima party, said they were committed to making progress in terms of agreeing a settlement.
Elusive peace
Al Jazeera's Nour Odeh, reporting from Cairo, said: "What is interesting here ... is that the Quartet has decided to forbid itself from exercising control to make the parties talk.
"They are letting the sides talk it out on their own, yet their mandate is to somehow enforce dialogue. It reflects the stance of the Quartet, that perhaps peace really is elusive here and another approach may be needed."
Last November in Annapolis, Israeli and Palestinian leaders revived negotiations aimed at resolving core problems such as the status of Jerusalem, the borders of a future Palestinian state and the right of return for Palestinian refugees.
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| Israeli and Palestinian leaders continue to be at odds over final status talks [AFP] |
Despite the upcoming transition of power, the Bush administration secured a commitment that the process begun in Annapolis would continue.
"I believe that the Annapolis process is now the international community's answer and the parties' answer to how we finally end the conflict between the Palestinians and the Israelis," Rice said at a news conference after the talks.
Blair urged Obama to carry on with the process, despite signs that some members of the new president's team may want to try a different approach. Even Russia, which has increasingly been at odds with the US, said that completing the process begun by the Bush administration is important.
Sergei Lavrov, the Russian foreign minister, said: "Our common desire is to make sure the Annapolis process succeeds."
Al Jazeera's Amr el-Kahky, reporting from Sharm el-Sheikh, said that the Palestinians were determined to seal a deal.
"But bear in mind there is a vacuum in Palestinian politics, as well as the current political turmoil in Israel. Therefore, it is very diffcult for any progress to be made."
Reconciliation talks between Hamas, Fatah and other Palestinian factions which were due to take place on Monday in Cairo, the Egyptian capital, had been cancelled on Saturday.