Tony Blair has predicted that George Bush will re-engage in Middle East peace efforts if the ground is prepared for a viable Palestinian state.
Tony Blair recently met Israeli Prime Minister Ariel Sharon in Jerusalem
The US president was committed to securing peace between Israel and the Palestinians, the prime minister said.
If Britain helped the Palestinians develop the "basic infrastructure of a viable state", then President Bush would make it viable territorially.
The work would begin at a London-based peace conference in March, he said.
However, the Israeli government has already said it will not be attending the summit.
"If we can get that conference successfully moving ahead and then the Israelis disengage from part of the occupied territories, then I believe that President Bush will be willing in those circumstances to get back into the roadmap and get back into the
conferences that can lead to a proper final status resolution," Mr Blair said.
Mr Blair has repeatedly highlighted the importance of resolving the Palestinian question to the security of the Middle East and the wider world.
He told BBC1's Breakfast With Frost: "In my view... a settlement of the Palestinian issues, democratic elections in Iraq, democracy in Afghanistan are central parts, not just of security out there in that part of the world, but
security here in this country."
He said: "For the first time in a long time we have got the possibility of progress here.
"We have got a new Israeli government that is committed to reinvigorating the peace process and we've got a new Palestinian leadership that is committed to the same thing."
The comments come as Palestinians head to the polls to elect a successor to their deceased president Yasser Arafat.
Palestinian Liberation Organisation chairman Mahmoud Abbas is the front-runner in the race to succeed Mr Arafat.
He is widely considered to have been the main architect of the Oslo Peace Accord which came close to resolving the conflict in the early 1990s.