A senior Palestinian negotiator, Saeb Erekat, said: "We have this opportunity now, and I hope we are not going to waste it. . . I think we will win the day."

But the mood in Jerusalem and other cities in the Holy Land was more subdued. Jonathan Kuttab, a Palestinian Christian and a former negotiator in talks with Israel, said: "I am wary of the Annapolis agreement. It's important to make a distinction between speeches and facts on the ground. I am not overly optimistic."

Nevertheless, Mr Kuttab continued, "both sides want peace; so we must be hopeful. Hope is a spiritual quality, a belief that somehow the level of violence and the evil of the occupation can't last for ever."

The initial agreement reached on Tuesday envisages Israel, the Palestinians, and the US engaging in "vigorous, ongoing, and continuous" efforts to reach a peace deal by the end of 2008. This target is ambitious, to say the least. Decades of diplomatic effort have failed to resolve any of the core issues.

While newspapers in the West Bank supporting Mr Abbas exuded optimism, describing the talks as the first step towards a Palestinian state, a very different atmosphere prevailed in the Gaza Strip.

Here, at least 100,000 Hamas supporters demonstrated to denounce the Annapolis meeting and all who were taking part in it. "Let them go to a thousand conferences," a Hamas leader told a rally. "We did not authorise anyone to sign any agreement that harms our rights. Anyone who does so will be judged by history as a traitor."

With the Palestinian community split, Mr Abbas's room for manoeuvre and compromise is constricted. Any sign that he is ready to give ground on the "key issues" - the future of Jerusalem, borders, water, the right of return of Palestinian refugees, and the future of Jewish settlements - will be seized on by his opponents.

Mr Olmert will also be under pressure from the far right in Israel to stand firm on all these issues. His main political rival, Benjamin Netanyahu, dismissed the Annapolis summit as "a continuation of one-sided concessions" to the Palestinians.

If the process can get under way in the coming months, then, according to the agreed statement, "implementation of the future peace treaty will be subject to the implementation of the Road Map, as judged by the United States". So there appears to be a serious commitment at last by the US administration to becoming actively involved in the peace process.

But one of the conditions of the Road Map for peace is that the Palestinians guarantee security on the ground and the Israelis restrict settlement activity. One terrorist attack by a radical Palestinian group could put the process under strain - as could Israel's failure to dismantle settlements.

Perhaps the biggest challenge for Arab and Israeli leaders will be to win public confidence in the process. It looks at this stage like a tall order - but not necessarily an impossible one.