Bush: "I've given it my all"
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Voters have been going to the polls in the United States to cast their ballots in one of the tightest presidential elections in recent history.
Final opinion polls showed George W Bush - who cast his vote in Texas - and John Kerry in a virtual dead heat.
Analysts predict the highest turnout for 40 years and both candidates were still campaigning on election day.
With the race so close, there are fears of a repeat of 2000's disputed result and subsequent legal wrangling.
In Florida, thousands of lawyers from the two political parties, as well as international election observers, have been drafted in amid reports of lost ballots, confusing voter technology and intimidation of voters.
However, Mr Bush and Mr Kerry have both said they do not think a protracted legal battle is likely.
The first votes to be cast and counted on election day were on the east coast, in New Hampshire's North County, where a survey of a few dozen voters showed a narrow lead for Mr Bush.
Pulling up at a polling station in Crawford, Texas, the sitting president acknowledged applause before going inside.
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SWING STATE ELECTORAL COLLEGE VOTES
1. Florida - 27 electoral votes
2. Pennsylvania - 21
3. Ohio - 20
4. Minnesota - 10
5. Wisconsin - 10
6. Iowa - 7
7. Nevada - 5
8. New Mexico - 5
9. New Hampshire - 4
Electoral college map
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"I've given it my all," he told reporters when he re-emerged, flanked by Laura Bush. "Who do you trust? I trust the judgment of the American people."
He was due to visit supporters in Columbus, Ohio, before going on to Washington.
Mr Kerry stopped off in La Crosse in the swing state of Wisconsin on Tuesday, on his way home to Boston, where he will vote himself and wait for the result.
"Together we are going to put common sense and truth back into the decisions of this nation," he told a rally.
As well as choosing their next president, Americans are also electing a new 435-seat House of Representatives, while voters in 34 states will be choosing new senators.
Swing state tension
Although a reported two million people have already cast their ballots in Florida during two weeks of advance polling, turnout was expected to be heavy on election day.
On Monday, people in some parts of Florida queued for several hours to take advantage of the last day of early voting.
Tensions are also high in the state of Ohio, which like Florida could prove decisive in the poll outcome.
Even a narrow majority would give the winner the state's entire set of 20 Electoral College votes that are used to pick the president.
Just hours before the polls opened, a federal appeals court in Ohio cleared the way for political party observers in polling stations to challenge the credentials of voters.
A lower court had ruled that such observers should be barred, after African-Americans argued that plans by President Bush's Republican Party to deploy them in mainly black areas amounted to intimidation.
Democrats have appealed to the US Supreme Court against the latest decision.
The BBC's Rob Watson in Washington says a higher than usual turnout may benefit Mr Kerry, as first-time and occasional voters are more likely to vote for change.
However, Americans are not in the habit of changing leaders during war time and may in the end decide to stick with Mr Bush, our correspondent adds.