Although Israel has welcomed the idea of returning to so-called "proximity talks" the Palestinians have not yet agreed to participate, insisting they will not enter any negotiations while Israel builds settlements on occupied land.
However, following the talks in the West Bank town of Ramallah, Palestinian officials said Washington's point man on the Middle East conflict had raised "ideas" for addressing the deadlock.
"Mitchell brought some US ideas," said Abbas spokesman Nabil Abu Rudeina, without going into detail.
"We will wait for the Arab Committee to discuss (them) and to decide," he said, referring to a meeting of Arab League foreign ministers in Cairo on Wednesday which Abbas is due to attend.
"We will continue discussions with the Arabs to decide the coming steps," Abu Rudeina said.
Shortly after the Ramallah meeting, Abbas set off for Cairo, a Palestinian official said.
Palestinian chief negotiator Saeb Erakat said the US ideas were the same as those raised when he met US Secretary of State Hillary Clinton in Washington last week.
During the meeting with Mitchell, Abbas had insisted that all Israeli settlement activity be frozen in the West Bank and annexed east Jerusalem, Erakat said.
"Anyone who talks about comprehensive peace must stop settlement building and Israeli activities," he said, referring to the US role of chief broker.
Talks began on September 2 but were suspended three weeks later with the end of an Israeli moratorium on settlement building, which the Jewish state has consistently refused to renew.
Ahead of the Ramallah meeting, a senior Palestinian source said they had been awaiting the US response to a list of conditions for a resumption of negotiations with Israel.
"Erakat delivered a letter to Clinton saying that they want US guarantees and answers before returning to any negotiations, direct or indirect," he told AFP. "We are now awaiting the answer to that letter."
But there was no mention of the letter nor of its demands in a joint Abbas-Mitchell press conference after their meeting, with the US envoy merely reiterating the US commitment to find a solution to the decades-old conflict.
"As we expected, there have been very many difficulties, obstacles and setbacks along the way," Mitchell said.
"We accepted it but we are determined to persevere in our efforts until we reach the conclusion that all want: an independent, viable state of Palestine ... living side by side in peace with Israel."
The letter had laid out two key requests on which the Palestinians are conditioning their return to any peace talks with Israel.
Firstly, it seeks US guarantees that there would be "a complete halt to settlement in the West Bank and east Jerusalem."
It also calls for US recognition of a Palestinian state based on Israel's borders before the 1967 Six-Day War in which the Jewish state seized the West Bank, the Gaza Strip and east Jerusalem.
If Washington refuses, the letter asks that it not take steps to block the Palestinians from seeking such recognition from the UN Security Council.
Mitchell on Monday held talks with Israeli Prime Minister Benjamin Netanyahu, who has made no secret of his satisfaction that the focus had been taken off settlement activity and placed firmly on core issues.
On Tuesday, Netanyahu said he was keen to work towards a framework agreement linked to all the core issues.
"I had a good meeting yesterday with the American envoy George Mitchell. We spoke about concrete ways to push the peace process forward and reach a framework agreement for peace between us and the Palestinians," he said.
"That is Israel's goal and I hope the Palestinians will respond to it."
Meanwhile in Jerusalem, Israel approved the building of 24 new settler homes in the heart of a densely-populated Arab district of the city's eastern sector, in a move branded by settlement watchdog Peace Now as "a new provocation."
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