Republican presidential hopeful Mitt Romney has reignited controversy at a campaign rally over a discredited theory that President Barack Obama was not born in the United States and therefore not eligible to hold the country's highest office.

"No one's ever asked to see my birth certificate," Romney told a rally of some 7,000 people in his home state of Michigan.

"They know that this is the place that we were born and raised," he said to the laughter of the crowd, speaking alongside his wife, Ann.

The "birther" remarks drew a swift response from the Obama campaign, who said the candidate had "embraced" the most extreme conservative claims

The joke was a reference to the widely discredited belief that Obama, whose father was from Kenya, was not born in the United States and thus is not eligible to be president.

Conservative fringes of the Republican Party including high-profile Romney backer Donald Trump have argued that Obama was not born in Hawaii as he says.

In an effort to end the "birther" controversy, Obama has released multiple copies of his birth certificate that show he was born in the United States. But some conservatives refuse to let the issue die.

'Little humour'

"Governor Romney's decision to directly enlist himself in the birther movement should give pause to any rational voter across America," said Ben LaBolt, Obama campaign spokesman.

Brushing the comment off as a joke, the former Massachusetts governor said he did not believe the birther theories.

"I've said throughout the campaign and before, there's no question about where he was born. He was born in the US. This was fun ...and, you know we've got to have a little humor in a campaign," Romney told CBS News.

Romney's comments came as Republicans prepared for Monday's opening of a four-day convention that will formally nominate him for president, and were the latest detour from his central argument that Americans need a change from Obama's economic leadership.

It was the second time in as many days that Romney found himself under fire for comments on the campaign trial.

On Thursday, he said in Minnesota that "big business is doing fine in many places", partly because they benefited from offshore tax havens.