Media playback is unsupported on your device Media caption President Obama: "I can't tell you who I voted for"

President Barack Obama has cast his vote in his hometown of Chicago as his campaign seeks to boost early ballots in a neck-and-neck election race.

Mr Obama, who is on a two-day campaign marathon across eight states, is the first president to vote early.

His Republican challenger, Mitt Romney, is in Ohio, a swing state which could hold the key to the White House.

Thirteen days from the election, a new national poll says Mr Romney has 50%-47% support among likely voters.

The survey, produced for ABC News by Langer Research Associates, finds that when asked about which candidate they would trust more to handle the economy, 52% backed Mr Romney versus 43% for Mr Obama - the first time a candidate has held a clear lead on the issue.

Widespread early voting, as well as postal voting changes the game

The president's ballot casting on Thursday was part of his campaign's wider effort to encourage early voting, with many states holding open in-person polls this week.

First Lady Michelle Obama voted by absentee ballot on 15 October.

It is estimated that 7.2 million people have already cast early ballots, and that about 35% of the electorate will have already voted by polling day.

The Obama campaign also announced on Thursday that it backs gay marriage laws in three states that are holding referendums on the issue in November.

In Maryland and Washington, ballot measures are seeking to overturn gay marriage bills that were signed into law earlier this year. Meanwhile, Maine is voting on whether to reinstate a gay marriage law that was overturned in a popular vote in 2009.

Mr Obama first voiced support for the right of same-sex couples to marry in May.

Key states

Because the US election is a state-by-state contest, a presidential candidate must win key battlegrounds like Ohio, Virginia and Florida, which do not reliably vote for either party. No Republican has ever won the White House without taking Ohio.

The Obama campaign recently won a court ruling to keep Ohio's early voting open through the weekend before the election.

Media playback is unsupported on your device Media caption Obama spoke about the Mourdock controversy on late-night TV

Former Massachusetts Governor Romney made three stops across the Mid-Western state on Thursday, while his running mate Paul Ryan spent the day in Virginia.

But they have been distracted by the fall-out from a fellow Republican candidate's remarks on Tuesday night that pregnancy from rape was part of God's plan.

The Romney campaign has said it disagreed with the comments by anti-abortion Indiana Senate hopeful Richard Mourdock, although it did not withdraw support from him.

"We disagree on the policy regarding exceptions for rape and incest, but still support him," a campaign spokeswoman said.

Republicans running in tight contests elsewhere have repudiated Mr Mourdock's remarks.

Mr Obama criticised Mr Mourdock on a US late-night talk show on Wednesday.

"I don't know how these guys come up with these ideas... rape is rape. It is a crime," Mr Obama told host Jay Leno, adding that politicians had no business making decisions for women about their bodies and health choices.

On Thursday, the president makes campaign stops in Florida, Virginia and Ohio. On Monday, he will appear for the first time at a campaign event this election cycle with former President Bill Clinton.

In an interview with the Des Moines Register, Mr Obama indicated what issues would be his priority in a second term, including a budget deal to reduce the US debt, as well as immigration.

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Mr Obama received a boost from Colin Powell, formerly Secretary of State for Republican President George W Bush, who endorsed the president on Thursday.

Mr Powell, who also backed Mr Obama in 2008, cited recent improvements in the economy and Mr Obama's guidance of the US military as reasons for his renewed support.

"I also saw the president get us out of one war, start to get us out of a second war and did not get us into any new wars." Mr Powell said, adding that under Mr Obama the US economy was "out of the dive and starting to gain altitude".

He also expressed doubts over Mr Romney's approach to foreign policy, saying the candidate's policies were a "moving target".