Palestinian leader Mahmoud Abbas has offered "the hand of peace" to Israel after his landslide victory in Sunday's presidential election.
Mahmoud Abbas needed a strong mandate, analysts said
"We are ready for peace, peace based on justice. We hope that their [Israel's] response will be positive," he said.
Mr Abbas urged a resumption of talks based on the internationally-backed "roadmap" peace plan.
President Bush has invited him to visit Washington - something he denied Mr Abbas' predecessor Yasser Arafat.
Mr Bush told the new Palestinian leader that he was committed to helping him work towards creating a free and democratic Palestinian state and tackling key issues such as security, terrorism and economic growth.
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
"I offer my congratulations to Abu Mazen... I look forward to welcoming him here to Washington if he chooses to come here," Mr Bush said in a telephone call.
He added that he envisioned "a day when he and president-elect Abbas and Israel's leaders could stand together and say, 'We have peace'," the White House said.
Mr Bush also urged Israel to "fulfil its obligation on the withdrawal from the territories that they have pledged to withdraw from".
Preliminary official results show that Mr Abbas won 62.3% of the vote in the poll to succeed the late Yasser Arafat.
Mr Abbas' main rival Mustafa Barghouti got 19.8%. Admitting defeat, he said it was a victory for Palestinian democracy.
Israel has welcomed the result of the Palestinian poll 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.
"He [Mr Abbas] will be tested by the way he battles terror and acts to dismantle its infrastructure," Mr Sharon said.
Mr Abbas had earlier indicated he wanted 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.
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.