The Palestinian leader met US Middle East envoy George Mitchell at a New York hotel before talks with other Arab leaders, a Palestinian source said.
The US administration also remained in touch with Israeli leaders, according to State Department spokesman P.J. Crowley.
"We are doing everything we can to keep the parties in direct talks," Crowley said in a Twitter message.
Abbas met US Secretary of State Hillary Clinton on Friday night, and in Washington, US President Barack Obama kept his schedule largely free so he could take calls, officials said.
Israel's Defense Minister Ehud Barak and Yitzhak Molcho, Prime Minister Benjamin Netanyahu's point man on the peace talks, were also in New York to aid compromise efforts, Israeli radio reported.
Israel's freeze on building new settlements in the West Bank expires at midnight on Sunday. The Israeli government has rejected strong international calls to completely halt settlement construction.
A senior Israeli official said Friday that "there cannot be zero construction" in the West Bank. The official said Israel was willing to cut a compromise deal.
But Abbas rejected any compromise that does not guarantee a "complete halt" to settlement activity including in Jerusalem, a top aide, Nabil Abu Rudeina, told AFP.
In a speech to the UN General Assembly, the Palestinian leader praised Obama's efforts to bring Israelis and Palestinians together and declared his "complete readiness to cooperate with the American efforts for the success of the political process."
He said Palestinians face "dangerous problems that continue to push them into the corner of violence and conflict, wasting chance after chance to seriously address the issues faced by the people of the region and to attain comprehensive and genuine solutions.
"This is the result of the mentality of expansion and domination, which still controls the ideology and policies of Israel."
Abbas added that Palestinians still want peace and declared: "Our wounded hands are still able to carry the olive branch from the rubble of the trees that the occupation uproots every day."
The deadline for the freeze to end is widely accepted as Sunday, 10 months and a day after an original Israeli cabinet decision expires. A military order on the moratorium states it will only close on October 1.
Jeffrey Feltman, assistant secretary of state for Near East affairs, echoed a toughening US line toward the two sides.
"We are urging Israel to extend the moratorium," Feltman said. "We also are making clear to the Palestinians we do not believe that it is in their interest to walk out of the talks."
Obama restated demands for the moratorium to be extended and issued a strong call at the General Assembly on Thursday for the world to back his peace drive.
US officials have suggested a three-month extension to the moratorium, during which time Israel and the Palestinians could agree on borders, potentially neutralizing the settlements dispute, a senior Palestinian official said.
The international community considers Jewish settlements in the West Bank, including annexed east Jerusalem, to be illegal.
Some 500,000 Israelis live in more than 120 settlements across the West Bank and east Jerusalem, territories expected to form the bulk of a future Palestinian state.
The previous round of direct negotiations collapsed when Israel launched a military offensive on the Hamas-run Gaza Strip in December 2008, aimed at halting rocket and mortar attacks.
Highlighting challenges to the new process, on Saturday a rocket fired from the Hamas-controlled Gaza slammed into southern Israel, without causing casualties, according to an army spokeswoman.
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The US administration also remained in touch with Israeli leaders, according to State Department spokesman P.J. Crowley.
"We are doing everything we can to keep the parties in direct talks," Crowley said in a Twitter message.
Abbas met US Secretary of State Hillary Clinton on Friday night, and in Washington, US President Barack Obama kept his schedule largely free so he could take calls, officials said.
Israel's Defense Minister Ehud Barak and Yitzhak Molcho, Prime Minister Benjamin Netanyahu's point man on the peace talks, were also in New York to aid compromise efforts, Israeli radio reported.
Israel's freeze on building new settlements in the West Bank expires at midnight on Sunday. The Israeli government has rejected strong international calls to completely halt settlement construction.
A senior Israeli official said Friday that "there cannot be zero construction" in the West Bank. The official said Israel was willing to cut a compromise deal.
But Abbas rejected any compromise that does not guarantee a "complete halt" to settlement activity including in Jerusalem, a top aide, Nabil Abu Rudeina, told AFP.
In a speech to the UN General Assembly, the Palestinian leader praised Obama's efforts to bring Israelis and Palestinians together and declared his "complete readiness to cooperate with the American efforts for the success of the political process."
He said Palestinians face "dangerous problems that continue to push them into the corner of violence and conflict, wasting chance after chance to seriously address the issues faced by the people of the region and to attain comprehensive and genuine solutions.
"This is the result of the mentality of expansion and domination, which still controls the ideology and policies of Israel."
Abbas added that Palestinians still want peace and declared: "Our wounded hands are still able to carry the olive branch from the rubble of the trees that the occupation uproots every day."
The deadline for the freeze to end is widely accepted as Sunday, 10 months and a day after an original Israeli cabinet decision expires. A military order on the moratorium states it will only close on October 1.
Jeffrey Feltman, assistant secretary of state for Near East affairs, echoed a toughening US line toward the two sides.
"We are urging Israel to extend the moratorium," Feltman said. "We also are making clear to the Palestinians we do not believe that it is in their interest to walk out of the talks."
Obama restated demands for the moratorium to be extended and issued a strong call at the General Assembly on Thursday for the world to back his peace drive.
US officials have suggested a three-month extension to the moratorium, during which time Israel and the Palestinians could agree on borders, potentially neutralizing the settlements dispute, a senior Palestinian official said.
The international community considers Jewish settlements in the West Bank, including annexed east Jerusalem, to be illegal.
Some 500,000 Israelis live in more than 120 settlements across the West Bank and east Jerusalem, territories expected to form the bulk of a future Palestinian state.
The previous round of direct negotiations collapsed when Israel launched a military offensive on the Hamas-run Gaza Strip in December 2008, aimed at halting rocket and mortar attacks.
Highlighting challenges to the new process, on Saturday a rocket fired from the Hamas-controlled Gaza slammed into southern Israel, without causing casualties, according to an army spokeswoman.
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