Mr Trump told reporters he had “heard” suggestions that Ms Harris – who is Democratic candidate Joe Biden’s running mate – was born to immigrant parents and could not serve in the White House.
The conspiracy about Ms Harris, which is part of an online misinformation campaign, bears similarity to one Mr Trump used to power his rise into politics.
Ms Harris’s mother was born in India and her father was born in Jamaica and she was born in Oakland, California, and is eligible to be president and vice president under the constitutional requirements.
“I have no idea if that’s right,” said Mr Trump, who said he had read a column on the subject earlier on Thursday.
“I would have thought, I would have assumed, that the Democrats would have checked that out before she gets chosen to run for vice president.”
Mr Trump made the comments in answer to a reporter’s question and appeared to be referencing an piece written by John Eastman, a conservative lawyer who argues that the US Constitution does not grant citizenship to all people born in the US.
The president’s re-election campaign’s senior lawyer, Jenna Ellis, shared the controversial column on Thursday morning, hours before Mr Trump was asked about it at a White House news conference.
Mr Trump noted that the column was written by a “very highly qualified and very talented lawyer”.
But the question is not considered complex, according to lawyers who have reviewed her circumstances.
Jessica Levinson, a professor at Loyola Law School, said: “Full stop, end of story, period, exclamation point.
“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.”
Mr Trump built his political career on questioning a political opponent’s legitimacy.
He was a high-profile force behind the so-called “birther movement” – the lie that questioned whether president Barack Obama, the nation’s first black president, was eligible to serve.
Only after mounting pressure during his 2016 campaign did Mr Trump disavow the claims.
Mr Trump comments about Ms Harris on Thursday came amid a series of untrue, racist or sexist claims unleashed across social media and conservative websites after Mr Biden picked Ms Harris, the first black woman and the first Asian American woman on a major party ticket.
The misinformation campaign is built on falsehoods that have circulating less noticeably for months, propelled by Mr Trump and his supporters.
