In response to Abbas, Rice said that the road map was the way towards a lasting solution.
"My work is going to be best targeted, I think, in these next months on trying to accelerate progress on the road map, which after all would lead us then to a Palestinian state and to helping the Palestinians and Israelis think through the political horizon," she said.
"The Palestinian people have waited a long time for their own state. The Israeli people have waited a long time to live in security and peace with their neighbours"
Condoleezza Rice, US secretary of state
She also said that the United States needed to deepen its involvement in Middle Eastern peace efforts.
"You will have my commitment to do precisely that," she said.
"The Palestinian people have waited a long time for their own state. The Israeli people have waited a long time to live in security and peace with their neighbours," Rice said.
Mohammed Dahlan, an Abbas confidant, said after the meeting that Rice "showed understanding" for the Palestinian position.
However, Rice did not consult any member of the democratically elected Hamas Palestinian government during her trip.
Ghazi Hamad, a Hamas spokesman, said the US policy of backing Abbas and ignoring Hamas was "doomed to fail because the Palestinian people are not bought with money, and no one believes that trying to lure some [Palestinians] will lead to results".
"American policy has not changed for a long time, and it attempts to create rifts between the parties," he said.
Abbas said he will aim to go ahead with early elections if current coalition talks with the Hamas government fail.
However, Abbas said it was too early to talk about a meeting between him and Khaled Meshaal, Hamas's leader, who is based in Syria.
Abbas is to visit Syria later this month.
"Unless the US administration is prepared to read the riot act to the Israeli government... nothing will be achieved"
Nehad Ismail, London, UK
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The Palestinian leader said early elections are still an option. "We hope and we work to achieve this [a unity government] as soon as possible," he said. If not, "we will return to the people and hold the early parliamentary and presidential elections," he added.
Rice's meeting with Abbas followed talks on Saturday, Livni, and Amir Peretz, the Israeli defence minister.
Last month, Livni proposed setting up a provisional Palestinian state, with a border based on the separation barrier Israel is building in the West Bank.