Interim Palestinian leader Mahmoud Abbas has won a landslide victory in Sunday's presidential election to succeed the late Yasser Arafat.
Mahmoud Abbas needed a strong mandate, analysts said
Preliminary official results show that Mr Abbas won 62.3% of the vote on a turnout of about 66%.
His main rival Mustafa Barghouti got 19.8%. Admitting defeat, he said it was a victory for Palestinian democracy.
Israel has welcomed the result and urged Mr Abbas to clamp down on militant Palestinian groups.
"The main focus at this stage... should be Palestinian action on terror," said Israeli Prime Minister Ariel Sharon in a statement.
Moderate head of main political faction Fatah
Seen as someone Israel will talk to
Willing to talk peace with Israel
Wants end to Palestinian armed uprising
Pledges to stick to key positions of late Yasser Arafat
"He [Mr Abbas] will be tested by the way he battles terror and acts to dismantle its infrastructure," Mr Sharon said.
Mr Abbas has indicated he wants to meet Mr Sharon as soon as possible.
Israeli officials say Mr Sharon is prepared to hold security talks with the new Palestinian leader, but full-scale peace negotiations will have to wait.
US President George W Bush has said he will invite Mr Abbas (also known as Abu Mazen) to Washington - something he refused to do with his predecessor, the late Yasser Arafat.
"I offer my congratulations to Abu Mazen. I look forward to talking to him at the appropriate time. I look forward to welcoming him here to Washington if he chooses to come here," Mr Bush said.
He noted Mr Abbas had been elected with "a good-size majority".
Earlier, Mr Bush said it was, along with upcoming parliamentary polls, "essential for the establishment of a sovereign, independent, viable, democratic and peaceful Palestinian state that can live alongside a safe and secure Israel".
The EU has also praised the election.
"It is a very important step towards the creation of a viable and democratic Palestinian state," said European Commission President Jose Manuel Barroso.
The head of the European Union election monitoring team, former French Prime Minister Michel Rocard, said it was "unique in the world to have general elections conducted democratically under foreign military occupation".
Soul of Arafat
Full results will be published once all complaints have been assessed, Central Election Commission head Hanna Nasser told reporters.
Analysts had said Mr Abbas needed a large margin of victory to push his agenda of peace talks with Israel.
Mr Abbas addressed a rally of hundreds of supporters in the West Bank town of Ramallah to dedicate his victory to Mr Arafat.
"I present this victory to the soul of Yasser Arafat and present it to our people, to our martyrs and to 11,000 prisoners" in Israeli jails.
Mr Abbas also called on militant Palestinian groups, who boycotted the election, to end their armed uprising against Israeli occupation.
A Hamas representative, Mahmoud Zahar, told the BBC that the new president would not succeed because Israel would not give him a chance. But Hamas says it will work with Mr Abbas, despite boycotting the poll.
Voting was reported to have been brisk but there were problems with registration, heavy turnout and the turning-away of hundreds of voters from a big Israeli-run polling station in East Jerusalem.
Some chaotic scenes were reported there.
Voters complained that Israeli officials were not allowing them to vote even though the Palestinian central election commission had properly registered them.
Although voting seemed to go smoothly for most of the day in Gaza, there were reports of chaotic scenes outside polling stations in the evening.
At a polling station in Ramallah in the West Bank, five Palestinian gunmen fired into the air in frustration that some names had been left off lists.
They were persuaded to leave the station.