In an interview with the BBC, reported on the news agency's website, Prime Minister Ehud Olmert said Israel was prepared to "pull out from many, many territories".
During the interview, he reaffirmed his support for a Palestinian state and said a new border would have to be determined, "hopefully through negotiations".
"I'm making extraordinary efforts now to try and reach that kind of understanding with Abu Mazen that will allow both of us to start open, bilateral negotiations," Olmert told the BBC.
He said he was "very hopeful" that talks would go ahead "in spite of the difficulties that he (Abbas) experiences all the time".
Abbas has called for peace talks with Israel and is considered well-intentioned by Israeli officials. However, he is restricted by the radical and inflexible party line taken by the Hamas-led government.
According to Olmert, talks would not be easy because the Palestinian Prime Minister, Hamas' Ismail Haniyeh, was "not prepared to make any move towards peace".
Hamas has repeatedly and openly resisted international calls to reject violence and recognize Israel. In his recent visit to Tehran, Haniyeh pledged "never (to) recognize the usurper Zionist government and…continue our jihad-like movement."