President Barack Obama and Republican challenger Mitt Romney were this morning running neck and neck in the race for the White House.

Three of the early critical battleground states which will decide the result – Virginia, Ohio and Florida – were too close to call.

First reports showed Obama with a 3% lead in Ohio and a 1% lead in Florida, while in Virginia the two men were tied.

Romney needs all three to win the presidency, while Obama can afford to lose one or two of them and still win a second term.

No Republican has ever captured the White House without carrying Ohio.

At least 120million people turned out to vote, only days after many north-east US states were ravaged by Hurricane Sandy.

Election Day capped an aggressive, negative and vastly expensive campaign.

And although the President was reported to be holding slim leads in many of the eight swing states that will determine the winner, there is still a possibility of a repeat of the 2000 election when the winner, George W Bush, was not known for weeks after a protracted recount in Florida and a Supreme Court decision.

Apart from Florida, Ohio and Virginia, the key bellweather states are Wisconsin, New Hampshire, Iowa, Colorado and Nevada.

A narrow victory for either candidate is also likely to leave the winner without a strong mandate to face mounting problems – including higher taxes and deep automatic cuts in spending that loom in January if Republicans and Democrats in Congress cannot reach an accord on US finances.

Obama played basketball in a gym near his Chicago home as millions of Americans waited in long lines to cast their ballots.

Earlier he was met with applause and tears from volunteers as he entered a campaign office before picking up a phone to call voters.

He congratulated Romney on a "spirited campaign" and told reporters he's "confident we've got the votes to win, but it's going to depend ultimately on whether those votes turn out".

Romney and family were at his home near Boston to wait for the results after making two last campaign stops with running mate Paul Ryan in Ohio and Pittsburgh, Pennsylvania.

No Republican has ever captured the White House without carrying Ohio.

It was not just the presidency at stake. All 435 seats in the House of Representatives, a third of the 100 Senate seats and 11 governorships were on the line, along with ballot proposals in some states on topics ranging from gay marriage to legalising marijuana.

Democrats were expected to maintain their majority in the Senate, with Republicans doing likewise in the House, raising the prospect of continued partisan wrangling no matter who might be president.

The economy has proved a huge drag on Obama's candidacy as he fought to turn it around after the deepest recession since the Great Depression of the 1930s, a downturn that was well under way when he replaced Bush.

No US president since Franklin D Roosevelt in the 1930s has run for re-election with a national jobless rate as high as it is now – 7.9% in October.

Romney has worked doggedly to keep the race focused on the economy, and polls suggest that he succeeded in persuading many Americans he has the right credentials to steer America to better times.