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President Donald Trump says he has heard Democratic running mate Kamala Harris "doesn't qualify" to serve as US vice-president, amplifying a fringe legal theory critics decry as racist.
Ms Harris was born to a Jamaican father and Indian mother in Oakland, California, on 20 October 1964.
But a constitutional law professor has questioned her eligibility.
For years, Mr Trump promoted a false "birther" theory that President Barack Obama was not born in the US.
Ms Harris, a California senator, was unveiled on Tuesday as the first woman of colour to serve as running mate on a main-party presidential ticket.
She is deputy to Democratic White House candidate Joe Biden, who will challenge Mr Trump, a Republican, in November's general election.
What did Trump say?
At Thursday's press conference, Mr Trump was asked about the argument against Ms Harris.
The president said: "I just heard it today that she doesn't meet the requirements and by the way the lawyer that wrote that piece is a very highly qualified, very talented lawyer.
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"I have no idea if that's right. I would have assumed the Democrats would have checked that out before she gets chosen to run for vice-president.
"But that's a very serious, you're saying that, they're saying that she doesn't qualify because she wasn't born in this country."
The reporter replied there was no question that Ms Harris was born in the US, simply that her parents might not have been legal permanent residents at that time.
Earlier on Thursday, a Trump campaign adviser, Jenna Ellis, reposted a tweet from the head of conservative group Judicial Watch, Tim Fitton.
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In that tweet, Mr Fitton questioned whether Ms Harris was "ineligible to be Vice President under the US Constitution's 'Citizenship Clause'".
He also shared an opinion piece published in Newsweek magazine by John Eastman, a law professor at Chapman University in California.
What is the law professor's argument?
Prof Eastman cites Article II of the US Constitution's wording that "no person except a natural born citizen… shall be eligible to the office of President".
He also points out that the 14th Amendment to the Constitution says "all persons born… in the United States, and subject to the jurisdiction thereof, are citizens".
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Prof Eastman's argument hinges on the idea that Ms Harris may not have been subject to US jurisdiction if her parents were, for example, on student visas at the time of their daughter's birth in California.
In 2010, Prof Eastman ran to be the Republican candidate for California attorney general. He lost to Steve Cooley, who went on to be defeated by Ms Harris in the general election.
Following furious backlash to the Newsweek op-ed, its editor-in-chief Nancy Cooper stood by the decision to publish, arguing on Thursday that Prof Eastman's article had "nothing to do with racist birtherism".
What do other constitutional law experts say?
Another constitutional law expert told CBS News, the BBC's US partner, that Prof Eastman's argument about Ms Harris' eligibility was "truly silly".
Erwin Chemerinsky, the dean of Berkeley Law School, wrote in an email: "Under section 1 of the 14th Amendment, anyone born in the United States is a United States citizen.
"The Supreme Court has held this since the 1890s. Kamala Harris was born in the United States."
Laurence Tribe, a constitutional law professor at Harvard University and frequent critic of President Trump, called Prof Eastman's argument "garbage" and "racist birtherism redux".
Jessica Levinson, a professor at Loyola Law School, told the Associated Press news agency: "Let's just be honest about what it is: It's just a racist trope we trot out when we have a candidate of colour whose parents were not citizens."
How did Trump fuel the Obama 'birther' theory?
Back in 2011 Mr Trump began stoking right-wing theories that President Obama might have been born in Kenya.
Even when Mr Obama produced a copy of his birth certificate in April that year showing he was born in Hawaii, Mr Trump continued to claim it was a "fraud".
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During a September 2016 press conference Mr Trump, then the Republican White House candidate, was asked about the matter.
He sought to take credit for dispelling doubts over Mr Obama's eligibility, telling reporters: "I finished it. President Obama was born in the United States. Period."
Mr Trump also argued in 2016 that his election rival Ted Cruz was not eligible to run for president because he was born in Canada to a US citizen mother and a Cuban-born father.
