But Olmert stressed that securing the release of Gilad Shalit, the Israeli soldier abducted by Palestinian fighters from the Gaza Strip in June, was top of the agenda ahead of any meeting with Mahmoud Abbas.
Addressing a news conference with the British prime minister, Olmert said: "I assured prime minister Blair that I am ready to work closely with chairman of the Palestinian Authority Abbas to implement the road map."
Blair said he believed it would be possible to make progress on the road map, which has been held up by the failure of both Israelis and Palestinians to meet commitments.
Blair said: "It is very important that we see what we can do to reenergise this process.
"It's very easy to be pessimistic, but I do believe that, with the right will, things can be done."
Flying into Israel, Blair left behind feuding in Britain's ruling Labour party that forced him to concede this week that he will leave office within a year.
Blair's strong support for the US line during the Lebanon war fuelled dissent among some members of his Labour party that flared into open rebellion against him this week.
Blair will also meet Palestinian officials in coming days, sources in the region said.
Israel has killed more than 200 Palestinians, about half of them civilians, during an offensive in Gaza to try to free the soldier captured by fighters, who have demanded the release of Palestinian prisoners in exchange.
Olmert said he had been ready to free prisoners as a gesture to the Palestinians before Gilad Shalit was captured, in a possible hint that he could do so if the corporal was freed.
Olmert reiterated that the Palestinians had to meet a road map commitment to start disarming fighters, but Israel has failed to respect its own promise to freeze the building of Jewish settlements in the occupied West Bank.
Talks have looked even more unlikely since Hamas, whose charter calls for Israel's destruction, won elections earlier this year to take over the Palestinian government.
Yasser Abed Rabbo, an official with the umbrella Palestine Liberation Organisation, headed by Abbas, said any meeting should be "aimed at restarting the peace process".
Olmert acknowledged this week that he was shelving his centrepiece plan to unilaterally withdraw from parts of the occupied West Bank in the absence of peace negotiations with the Palestinians.