Blair wants Bush’s backing for a special conference of key Israeli and Palestinian figures to be held in London in the new year. The prime minister made clear last week he wanted the Arab-Israeli conflict to be a priority for Bush in his second term.

The chances of an agreement may have been enhanced by the condition of Yasser Arafat, the Palestinian leader, who is reported to be near death in a Paris clinic.

“A Middle East peace settlement is possible,” said a senior British government source. “Moderates on both sides know this. The prime minister knows resolving this issue is key to stopping terrorism.”

The meeting on Thursday and Friday will be Bush’s first post-election meeting with a foreign leader, underlining the close relationship between the two men.

Both Palestinian and Israeli officials accept Blair’s involvement in the peace process in the post-Arafat era. Britain wants to press Bush to ensure Israel returns to the “road map” and begins negotiations on a peace settlement.

Senior government sources said the starting point would be “filling in necessary details” in United Nations resolutions that look to the creation of a Palestinian state.

One suggested solution has been for the Israelis to give compensation to the Palestinians for their lost land rather than a right to return. An unofficial blueprint has been drawn up by Arab and Israeli peace negotiators in Geneva.

Details of Blair’s plan were revealed as it emerged that he came close to celebrating what he thought was a John Kerry victory. Blair saw unpublished exit polls on Tuesday wrongly suggesting the Democrat candidate was going to win. He telephoned John Prescott, the deputy prime minister, to discuss how to respond. He awoke at 5.30am to discover Bush had been re-elected.

Blair will face an uphill struggle to secure Bush’s attendance at such a conference. A source said: “I think Blair has had assurances from Bush that this is something he wants to move on. But Bush knows he will have to square matters at home.”

One uncertainty is Arafat’s condition. A spokeswoman yesterday denied he was brain dead. “He is in a coma,” said Leila Shahid, the Palestinian envoy to France.

Officials cautioned that no American initiative is likely until the Palestinians have agreed on Arafat’s successor. It is expected to be a moderate such as Mahmoud Abbas, former prime minister, or Ahmed Qureia, who currently holds the post. The stumbling block to a deal seems to be Bush’s reluctance to press Ariel Sharon, the Israeli prime minister, to offer concessions to the Palestinians.

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