Palestinian president Mahmoud Abbas has said he is ready for an "unconditional" meeting with his Israeli counterpart, after talks with the UK's Tony Blair.
Mr Abbas' announcement comes a day after Israeli Prime Minister Ehud Olmert also said he was prepared for talks without conditions.
Mr Blair stressed the importance of the Palestinians forming a government of national unity that recognised Israel.
There was a "window of opportunity" for both sides to engage in talks, he said.
The UK prime minister was speaking after meeting Mr Abbas in the West Bank town of Ramallah.
Mr Blair acknowledged that relations between the Palestinians and the Israelis are particularly bad right now, says the BBC's Alan Johnston, in Ramallah.
More than 200 Palestinians have died in recent fighting, many of them civilians.
In the latest violence on Sunday, one Palestinian teenager was killed and one wounded in an exchange of fire with Israeli forces in the southern Gaza Strip.
Nonetheless, Mr Blair urged the two sides to work to revive the peace process, and he committed himself to supporting any such effort.
"So far as I am concerned, this issue, which I believe passionately in, will be as important as any other priority for me in the time that remains for me in office," he said.
Mr Blair also urged Palestinians to form a government of national unity, which the international community could then deal with.
Western countries have been boycotting the Hamas-led government elected in January, because of Hamas' violent anti-Israeli stance.
The more moderate Mr Abbas leads Fatah, Hamas' rivals. He believes a coalition government of national unity would ease international pressure.
Correspondents say Mr Blair's remarks are the first suggestion that a broader Palestinian government, which still included Hamas, would be acceptable.
"I believe that such a government, based on the Quartet requirements, does offer the possibility of re-engagement by the international community," Mr Blair said.
But in a statement issued shortly after the Blair-Abbas news conference, Hamas rejected calls to moderate its anti-Israeli position.
Spokesman Sami Abu Zuhri said the group was ready to ready to form a coalition government with the more moderate Fatah movement, but "not according to standards that are dictated".
For his part, the Mr Abbas said he welcomed the prospect of talks with the Israeli prime minister, Ehud Olmert.
He said he wanted an "agreement of peace" which would lead to "two countries side by side".
Following a meeting with Mr Blair on Saturday, Mr Olmert had said that he was prepared to meet the Palestinian side, something that the Palestinians have been pressing for many months.
Mr Blair will not be meeting the leaders of the Hamas-controlled Palestinian government during his tour of the Mid-East.
A Downing Street spokesman said: "The purpose of this visit was to hear the views from all sides so we came here today to hear the views of the Palestinian president.
Mr Blair met with the families of captured Israeli soldiers
"He will bring with him the views he heard from Prime Minister Olmert and look to hear Palestinian views and Palestinian concerns and try to see how we can get back to some sort of dialogue."
Prior to his meeting with Mr Abbas, Mr Blair met with the families of Israeli soldiers seized by Islamic militants in Gaza and Lebanon.
A Downing Street spokesman said Mr Blair would raise the subject during his visit and hoped the men would be at home to celebrate the Jewish New Year later this month.