Meghan has been a vocal critic of the US president in the past and backed his political rival Hillary Clinton. Before the 2016 presidential election the duchess suggested she would leave the US if the former reality TV star Mr Trump won. In a recent interview with The Sun newspaper, Mr Trump claimed he was unaware of Meghan’s comments and said: “I didn’t know that. What can I say?
“I didn’t know that she was nasty.”
But in a Twitter post on Sunday, the president denied making the comment.
He wrote: “I never called Meghan Markle ‘nasty’. Made up by the Fake News Media, and they got caught cold!”
The President also expressed “doubt” that media organisations would “apologise”.
The Sun has posted an audio recording of the president’s interview with its political editor on its website.
In the interview, when asked about the duchess suggesting she would leave America for Canada if he was elected, Mr Trump said: “A lot of people are moving here to the US.”
Mr Trump said Meghan will make “a very good” American princess, and said of her joining the royal family: “It is nice, and I am sure she will do excellently.
“She will be very good. I hope she does succeed.”
The Sun recording is not the first time Mr Trump has used the word “nasty”.
During an election debate in 2016, he famously branded Democratic rival Hillary Clinton “such a nasty woman”.
As a result of Mr Trump’s latest remarks, opponents have been posting support for Meghan using the hashtag #nastywoman, which initially took after three years ago following the debate and has been used by his critics ever since.
One user said: “Congratulations to Meghan on achieving #nastywoman status! Go on lass.”
Another added: “I’m a #NastyWoman standing in support of Princess Meghan, the Duchess of Sussex. Bam!”
The Official Trump War Room account, which describes itself as being “managed by #Teamtrump 2020 campaign”, posted a link to a CNN story, commenting: “Fake News CNN is at it again, falsely claiming President Trump called Meghan Markle “nasty”. Here is what he actually said. Listen for yourself.”
Posters argued claims that the President had called Meghan nasty were “misleading”, suggesting instead he was simply referring to her comments about him.
Mr Trump begins his state visit to the UK on Monday and will meet members of the royal family, including the Queen.
LA-born Meghan will not be present during the visit after giving birth to her son Archie almost four weeks ago.