Abbas told a press conference in Ram Allah on Sunday following talks with Tony Blair, the visiting British prime minister:"I stand fully ready to meet with Prime Minister Ehud Olmert without prior conditions and we are ready to begin the preparations for such a meeting."
Olmert said on Saturday that he was also ready to meet Abbas to revive the moribund Middle East peace process.
Olmert and Abbas last met in an informal meeting in Jordan on June 23.
Blair told reporters the international community should deal with a future Palestinian unity government if it breaks with policies of the boycotted Hamas-led administration.
"I believe that such a government, based on the Quartet requirements, does offer the possiblity of re-engagement by the international community," Blair said.
"... if such a (unity) government is formed, then I believe that is right that the international community deal with such a government"
British prime minister
The Quartet of Middle East peace brokers - the United States, the European Union, the United Nations and Russia - has cut aid to the current Hamas-led government, demanding it recognise Israel, renounce violence and accept past interim peace deals.
"And I would like to say that so far as I'm concerned, that if such a (unity) government is formed, then I believe that is right that the international community deal with such a government," Blair said.
The British prime minister met Olmert, his Israeli counterpart, late on Saturday.
But Blair, received a cool reception on the streets of Ram Allah, where a demonstration has been called against his visit by groups who accuse him of pro-Israeli bias.
His office has already said his Middle East trip is unlikely to see any real breakthrough towards a peace process, but that it was important to help restart talks.
Olmert told Blair on Saturday that he was ready to meet Abbas - whom he last saw in an informal meeting in Jordan on June 23 - without preconditions, but did not set a date.
"I am ready to work closely with the chairman of the Palestinian Authority, Mahmud Abbas, to implement the road map," Olmert said.
In his meeting with Olmert, Blair urged both the Israelis and Palestinians to return to the roadmap, which has made next to no progress since it was launched in 2003.
"The only agreement that's ever going to stick ... is an agreement where people resolve their differences through politics and not through violence," he said.
"We have a plan to get there - the roadmap. We have to find a means of getting back to it," he said.
Drafted by the European Union, Russia, the United Nations and the United States, the roadmap sets out a series of steps necessary to establish a viable Palestinian state alongside a secure Israel.