Republican presidential nominee Donald Trump, who for years participated in the fringe "birther" movement questioning Barack Obama's nationality, is acknowledging that the US president is a native-born US citizen.

"President Barack Obama was born in the United States, period. Now we all want to get back to making America strong and great again," Trump said in an appearance at his company's newly opened hotel in Washington.

The US Constitution requires the president to be a citizen by birth.

Obama, the first African-American president, was born in Hawaii to married university students. His mother was a Kansas native, and his father was a foreign student from Kenya.

After Trump spoke, Democratic presidential nominee Hillary Clinton's campaign blasted his comments as "disgraceful."

"After five years of pushing a racist conspiracy theory into the mainstream, it was appalling to watch Trump appoint himself the judge of whether the president of the United States is American," Clinton campaign manager Robby Mook said. "This sickening display shows more than ever why Donald Trump is totally unfit be president."

Obama himself laughed off the issue, telling reporters he had "no reaction" to Trump's apparent reversal.

"I'm shocked that a question like that would come up at a time when we've got so many other things to do," Obama said before meetings Friday at the White House.

"Well, I'm not that shocked, actually. It's fairly typical. ... I was pretty confident about where I was born. I think most people were, as well. And my hope would be that the presidential election reflects more serious issues than that."

Trump, a New York billionaire with little previous political participation, blamed Clinton for rumours that started during Obama's 2008 presidential campaign.

"Hillary Clinton and her campaign of 2008 started the birther controversy," he said. "I finished it. I finished it - you know what I mean."

The respected website Politico reported in 2011 that the stories about Obama's birth arose among supporters of Clinton's failed 2008 bid for the left-leaning Democratic Party's presidential nomination, but there was no evidence of a direct tie to the Clinton campaign.

At the time, Obama had issued a document summarizing his birth record. In 2011, he allowed the release of his full Hawaii state birth certificate.

Trump, who had already been publicly encouraging the birther movement, claimed that his pressure had forced Obama to reveal the full document, which again debunked the allegations.

Since then, Trump had nurtured an ambiguous position on the place of Obama's birth.

Earlier Friday, Clinton, who served for four years as secretary of state under Obama, called for Trump to clearly repudiate his own history of questioning the president's nationality.

In a Washington speech, she said that Trump's campaign "was founded on this outrageous lie - there is no erasing it from history."

"Barack Obama was born in America, plain and simple. And Donald Trump owes him and the American people an apology," Clinton said.

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