In a tweet posted the day after the interview was published, he said the quote was “made up by the Fake News Media”.
“I never called Meghan Markle 'nasty',” he wrote. “Made up by the Fake News Media, and they got caught cold!
“Will @CNN, @nytimes and others apologize? Doubt it!”
When she was working as an actress Meghan described the US president as “misogynistic” and “divisive” and said she would be tempted to move to Canada if he won the US presidential election.
Asked about her comments, Mr Trump told the newspaper: "I didn't know that. What can I say?
"I didn't know that she was nasty."
The paper posted an audio recording of the original interview, proving that their reporting was accurate.
Mr Trump’s comments come ahead of his official state visit to the UK next week alongside his wife Melania and four adult children.
The US leader will be welcomed in the Buckingham Palace garden, before a state banquet in the palace’s ballroom on his trip which begins on Monday.
He is expected to meet the Queen, Prince Charles, Prince William and his wife, Kate, the Duchess of Cambridge.
Prince Harry will also meet the president, but Meghan will not be joining as she is currently on maternity leave with their son Archie.
The Duchess of Sussex has previously criticised Mr Trump and expressed support for his rival for the presidency, Hillary Clinton.
“You’re not just voting for a woman if it’s Hillary because she’s a woman, but certainly because Trump has made it easy to see that you don't really want that kind of world that he’s painting,” she said in a 2016 interview on The Nightly Show with Larry Wilmore.
Despite calling her “nasty”, Mr Trump said LA-born Meghan would make “a very good” American princess.
Asked for his thoughts on her joining the royal family, he said: “It is nice, and I am sure she will do excellently. She will be very good. I hope she does (succeed).”
He also said Boris Johnson would be “an excellent” prime minister, describing him as a “very good guy”.
It is highly unusual for a sitting US president to involve themselves in a UK political leadership contest and his comments risk sparking a diplomatic row.
Mr Trump also said he said he was “really loved” in the UK, adding: “I don’t imagine any US president was ever closer to your great land.”
However, as with last year’s visit, protesters are planning to take to the streets to express their opposition Mr Trump and his policies.
Scotland Yard said it has an experienced team ready to lead the huge police and security operation in response to the protests.
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