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Votes are still being counted in the key state of Florida where it seems there are only a few hundred votes separating the two would-be presidents.
Early exit polls claimed Republican George W Bush had taken the Sunshine State - but the claim was later retracted.
The Democrat White House hopeful, Al Gore, had apparently been on the verge of admitting defeat.
He had already phoned Mr Bush to offer his congratulations when he was told the Florida result was still too close to call.
Mr Gore telephoned Governor Bush a second time to withdraw his concession.
He said: "Circumstances have changed since I first called you.
"We have now learned we are down by only about 600 votes out of millions cast and that means an automatic recount."
The election campaign has been one of the closest for years.
National polls gave Governor Bush a slender lead as voters went to the polls but one survey gave Al Gore a two point advantage suggesting he could still win the race.
A high turnout of blacks and union members appears to have helped Mr Gore in the large industrial states.
Jeb Bush, Mr Bush's brother and governor of Florida, had promised to deliver the state for his brother.
The Texas governor appeared to hold a slender advantage in a string of swing states, including Missouri, Iowa, Wisconsin, Arkansas and Nevada.
If he wins in Florida, he will probably have enough electoral college votes to become president.
It is possible Mr Bush could win the electoral college but lose the popular vote. This has not happened since 1888 when Benjamin Harrison became President even though Grover Cleveland had amassed more votes.
Mr Bush closed his White House campaign by vowing to be a "uniter not a divider" if elected president and Mr Gore promised to "fight for you".
If Mr Bush were to win, he would be the first son of a former president to win the White House since John Quincy Adams was elected in 1824.
For Mr Gore, the son of a senator, victory would represent fulfilment of a childhood ambition and the culmination of 24 years as a congressman, senator and vice-president.
He ended his campaign with a whistle-stop tour of five states, ending in Florida. He was joined in Miami by celebrity supporters including actors Robert de Niro, Glenn Close, Ben Affleck and Stevie Wonder.
Texas Governor George Bush was eventually declared President-elect on 13 December 2000 after a protracted legal battle.
The vote in Florida went to a hand-count. But it turned out thousands of votes had been discarded by automatic machines because voters were supposed to knock out a small rectangle of card next to their choice of candidate and many were not punched properly.
The bits of card, known as chads, gave rise to serious complaints. Many black Americans claimed they had been disenfranchised after it was revealed the oldest and least reliable voting machines were placed in black precincts.
An inquiry carried out after the result had been decided concluded that more than 180,000 votes were thrown out as a result of poorly trained poll workers and a lack of standard procedures.
On 13 December 2000 Al Gore conceded victory to George W Bush.
It followed the Supreme Court's decision to impose a deadline for the recounts which, in effect, ruled out several thousand votes. It meant George W Bush won by just 537 votes out of a total of six million in Florida.
Al Gore did not stand for the 2004 presidential election - despite a vociferous campaign by supporters who wanted to see a re-match of the 2000 election.
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