United States Republican presidential nominee Donald Trump sparked fresh controversy late on Friday after he appeared to refer to the potential assassination of his Democratic rival Hillary Clinton for the second time.

"I think that her bodyguards should drop all weapons. Disarm immediately," Trump told a rally in Miami. "Take their guns away ... let's see what happens to her."

"Take their guns away, OK? It'll be very dangerous," he continued.

Clinton's campaign manager Robby Mook slammed the comments, saying they ought to be "out of bounds for a presidential candidate".

"Whether this is done to provoke protesters at a rally, or casually or even as a joke, it is an unacceptable quality in anyone seeking the job of commander in chief," said Mook in a statement quoted by CNN.

The comments came a month after Trump was accused of encouraging gun owners to assassinate Clinton if she wins the November 8 presidential election.

"Hillary wants to ... essentially abolish the Second Amendment," Trump said at a rally in North Carolina in early August, referring to the US Constitution's enshrinement of the right to bear arms.

"By the way, and if she gets ... to pick her judges, nothing you can do, folks. Although the Second Amendment people, maybe there is. I don't know," he continued.

Trump at the time denied the comments were an incitement to violence, saying he was encouraging guns rights activists to take to the ballot box and vote for him.

'Birther' Movement

Friday's comments came just hours after Trump, who for years had questioned Barack Obama's nationality as part of the Birther Movement, acknowledged for the first time that the president was 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.

Clinton's campaign blasted his comments as "disgraceful," while 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."

More reversals

While campaigning on Friday in South Florida, which has a large Cuban-American population, Trump also said that if he is elected president, he will reverse Obama's efforts to normalise relations with Cuba — unless the country abides by certain "demands".

Among those, he said, would be religious and political freedom for the Cuban people and the freeing of all political prisoners.

Trump says he will "stand with the Cuban people in their fight against communist oppression".

The comment marks yet another reversal for the Republican candidate, who previously said he supported the idea of normalised relations, but wished the US had negotiated a better deal.

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Trump also said that the US has a broader obligation to stand with oppressed people - a comment that seems at odds with his "America first" mantra.

"The next president of the United States must stand in solidarity with all people oppressed in our hemisphere, and we will stand with oppressed people, and there are many," he said.

He added that the people of Venezuela "are yearning to be free, they are yearning for help. The system is bad. But the people are great."

Trump has often cited the country as a model of a failed state, warning that if Clinton is elected, she will turn the US into Venezuela.