(Reposted from BBC)
Mr Trump said he had “heard” that Kamala Harris – a US-born citizen whose parents were immigrants – “doesn’t qualify” to serve as US vice-president.
The fringe theory has been dismissed by constitutional experts.
The Biden campaign called the comments “abhorrent” and “pathetic”.
They noted that Mr Trump spent years promoting a false “birther” theory that ex-President Barack Obama was not born in the US.
Ms Harris, a senator from California, on Tuesday became the first black woman and the first Asian-American to be named as a running mate on a main-party US presidential ticket.
“Donald Trump was the national leader of the grotesque, racist birther movement with respect to President Obama and has sought to fuel racism and tear our nation apart on every single day of his presidency,” a Biden campaign spokesman said in an email.
“So it’s unsurprising, but no less abhorrent, that as Trump makes a fool of himself straining to distract the American people from the horrific toll of his failed coronavirus response that his campaign and their allies would resort to wretched, demonstrably false lies in their pathetic desperation.”
Ms Harris was born to a Jamaican father and Indian mother in Oakland, California, on 20 October 1964. As such, she is eligible to serve as president or vice-president.
Constitutional scholars have dismissed the fringe legal theory that Mr Trump was referring to.
To be vice-president or president, Kamala Harris “has to be a natural-born citizen, at least 35 years old, and a resident in the United States for at least 14 years”, Juliet Sorensen, a law professor at Northwestern University, told the Associated Press news agency. “She is. That’s really the end of the inquiry.”
Anyone born in the US and subject to its jurisdiction is a natural born citizen, regardless of the citizenship of their parents, says the Cornell Legal Information Institute.
After a conservative law professor questioned Ms Harris’ eligibility based on her parents’ immigration status at the time of her birth, Mr Trump was asked about the argument at a press conference on Thursday.
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.