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U.S. President Barack Obama smiles during his election night victory speech in Chicago, Nov. 7, 2012.Kevin Lamarque/Reuters

Barack Obama has been re-elected President of the United States after a long, bitter and divisive battle with Republican challenger Mitt Romney.

Less than an hour after Mr. Romney conceded and stepped off the national political stage in Boston, Mr. Obama appeared before thousands of joyous supporters at his headquarters in Chicago.

"I just spoke with Gov. Romney and congratulated him on a fine campaign," he said, paying tribute to the Romney family. He also said he wanted to sit down with Mr. Romney in the coming weeks to discuss how they can work together.

Flanked by his wife Michelle and their daughters, Sasha and Malia, Mr. Obama took the the outdoor lakeside stage to thunderous cheers and chants of "four more years, four more years."

"We are an American family and we rise or fall together as one nation, one people," he said. "We have fought our way back ... and we know in our hearts, that for the United States of America the best is yet to come."

In an emotional victory speech launching his second term, Mr. Obama vowed – as he had done four years ago – to bridge the partisan divide that cleaves American.

Whether that re-kindled hope will prove more substantive in 2012 than it was in 2008 remains in doubt.

In Congress, Republicans retained control of the House of Representatives while Democrats keep their slim majority in the Senate.

With Mr. Obama back in the White House, the outcome of the election – one that cost more than $6-billion if all races are included – is a return to the status quo in Washington.

That raises the sorry prospect of more gridlock in Congress and an impasse between the Democrat President Obama and the Republican-dominated House of Representatives.

Earlier, Mr. Romney delivered a short and gracious concession speech in a subdued Boston hall. Beneath a Believe in America banner, the businessman who said America couldn't afford four more years of Mr. Obama ended a bid for the White House that was more than half a decade in the making.

"I pray that the president will be successful in guiding our nation," Mr. Romney, a devoutly religious Mormon, told cheering supporters, after telling them he had called the President to congratulate him on his victory.

Mr. Romney called for Americans – deeply divided again in another bitter election – to come together. "At a time like this we can't afford partisan bickering," he said.

Mr. Romney's defeat was sealed when Virginia – a 'must-win' state for the challenger and one that Mr. Romney had led most of the night – was lost to Mr. Obama. It was a defining loss, evidence that the changing demographics, especially the increasingly political importance of Hispanics, was re-shaping the American political landscape. (See our interactive map for full, state-by-state results)

Prime Minister Stephen Harper congratulated Mr. Obama on his re-election.

"I look forward to working with the Obama Administration over the next four years to continue finding ways to increase trade and investment flows between our countries," Mr. Harper said in a statement.

Americans voted Tuesday at polling stations from the storm-scarred eastern seaboard to Hawaii's volcanic islands and north of the Arctic Circle in Alaska. Long lines of frustrated voters waited in some Florida cities and in Virginia long after poll closing times, with some claiming hours-long waits.

Mr. Romney broke with election-day tradition and opted to campaign even as long lines of voters waited to cast their ballots.

"I can't imagine an election being won or lost by, let's say, a few hundred votes and you spent your day sitting around," the former Massachusetts governor told a radio audience in the key battleground state of Virginia before jetting to election-day appearances in Ohio and Pennsylvania.

The Obama campaign punched back, putting Vice-President Joe Biden on the blue-and-white Boeing 757 known as Air Force Two and sending him hurriedly to Cleveland. There – in an odd tableaus that illustrated the tipping-point focus on the bellwether state – both campaign aircraft were parked almost side-by-side as separate armoured motorcades took Mr. Biden and Mr. Romney off to rally partisans in a final get-out-the-vote effort.

Meanwhile, the president was playing basketball with a handful of aides at a Chicago recreation centre – an Election Day tradition for Mr. Obama – between a briefing on the flood relief effort and a visit to a Democratic call centre that didn't go quite as planned.

He made three impromptu calls; including one to a woman in Wisconsin who didn't seem to know who he was.

"This is Barack Obama. You know, the president?" the president explained, adding later after the call ended: "She seemed very nice."

The fight for the Oval Office – a $2-billion affair with more than one million TV ads, many of them unabashedly vicious – was fought mostly in nine battleground states: Ohio, New Hampshire, Virginia, Florida, North Carolina, Wisconsin, Iowa, Colorado and Nevada, worth a total of 110 Electoral College votes. The other 41 states were mostly ignored by the presidential rivals as they were considered safe for one or the other.

Not just the presidency was at stake.

One third of the 100 Senate seats, every one of the 438 House of Representatives and 11 governorships were on the ballot. In some states, like Florida, a plethora of local elections made for a 10-page ballot. Across the United States, voters were deciding on dozens of issues; from legalizing marijuana to approving casino gambling to – in Michigan – deciding on whether a new bridge to Canada should be built.

Early results from Michigan indicated the effort to block the bridge has failed.