As exit polls showed that Abbas had won some two-thirds of the votes cast, gunmen from his Fatah party were seen driving around the streets of the West Bank town of Ramallah firing in the air to celebrate his triumph.

"We dedicate this victory to the memory of our martyred leader Yasser Arafat, as well as all the other martyrs, those who have been wounded as well the 11,000 prisoners behind bars" in Israeli jails, an ecstatic Abbas told hundreds of his supporters.

"I will work to put an end to the suffering of the Palestinian people for they are a people who deserve our esteem, our respect and our loyalty."

The final result was due to be announced on Monday but Abbas' victory had never really been in any doubt, and Israel said that his biggest challenges now lay ahead if he wanted to become a partner in the peace process.

Voting was extended for two hours after the central elections commission said that Israeli restrictions in the occupied territories had hampered access to polling booths.

But monitors said there had been no major problems with what was the second ever presidential election here and that there were no reports of violence.

Prime minister Ahmed Qorei said the election underlined the Palestinian people's commitment to the path of peace and democracy.

"Today we have sent a crystal clear message to the world, to our people and to the region," said Qorei, who Abbas intends to reappoint as premier. "We, the Palestinian people, have shown that our choice is for peace and democracy."

US President George W. Bush also hailed it as an historic day for the Palestinian people.

"Palestinians throughout the West Bank and Gaza took a key step toward building a democratic future by choosing a new president in elections that observers describe as largely free and fair," Bush said in a statement.

The conduct of the ballot even won praise from Israel, which noted that it was a rare example of democracy in action in the region.

"I think to the best of my understanding and knowledge it's a democratic process and this in itself is enormously important because it's the only democratic process in the Arab world," said Deputy Prime Minister Ehud Olmert.

Abbas' nearest rival Mustafa Barghuti, who was projected to have won around 19 percent of votes, took a less positive view of the proceedings, charging that there had been blatant irregularities and that the supposedly indelible ink marked on the thumbnails of voters could be washed off with water.

Abbas's main fear had been that vast swathes of the electorate would heed a boycott call by the radical Islamist movement Hamas.

The elections commission said that around 70 percent of the 1.28 million registered voters cast their ballots.

But only around 10 percent of the other 700,000 Palestinians who were not on the register but who could still vote by presenting their identity card did so. That would leave the overall turnout among people eligible to vote below 50 percent.

Despite its call for a boycott, Hamas was making conciliatory noises.

Mahmud Zahar, leader in its Gaza Strip stronghold, said his movement could have run a candidate if it had really wanted to undermine Abbas.

"We could undermine Abu Mazen and others by naming our representative... so our opinion is not to undermine. Our system is always constructive, not destructive," he told reporters.

During his campaign, Abbas leant heavily on the legacy of his old boss Arafat even though the pair enjoyed an often tempestuous relationship.

Much of his campaign rhetoric has been straight out of the Arafat textbook with calls for the creation of an independent Palestinian state with east Jerusalem as its capital, the right of return for refugees and the release of all prisoners held by Israel.

But Abbas, who has already stepped up to take control of the PLO, also dotted his speeches with controversial criticism of the armed Palestinian uprising as well as hammering home his desire to implement long-delayed institutional reforms and end the security chaos on the streets of the West Bank and Gaza Strip.

An Abbas presidency is likely to lead to a resumption of top-level talks with Israel, frozen since he walked out after a short stint as Arafat's first premier in September 2003.

One of Sharon's senior aides said the prime minister was ready to meet the winner as soon as possible.

Deputy Prime Minister Olmert said that Abbas's real challenge was only just beginning, reiterating demands for him to crack down on militants.

"Now after being elected the main challenge is still ahead of him. Will he fight the terrorists and stop the bloody war against us?" he asked.

World leaders said the emergence of a new leader represented an important opportunity to advance the peace process.

"I think that for the first time in a long time we've got a possibility of progress here," said British Prime Minister Tony Blair."

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