The president’s comments were made after the Duke and Duchess of Sussex effectively endorsed Joe Biden in a recent video clip.
Donald Trump has taken a swipe at Meghan Markle after she and Prince Harry urged Americans to vote in the upcoming presidential election.
“I’m not a fan of hers,” the US president told reporters at a White House press briefing.
“I would say this – and she has probably has heard that – I wish a lot of luck to Harry because he’s going to need it,” he added.
It comes after the Duke and Duchess of Sussex effectively endorsed Mr Biden in a recent video clip for Time magazine.
Harry, 36, said: “It’s time to not only reflect, but act.”
“This election I’m not going to be able to vote here in the US, but many of you may not know that I haven’t been able to vote in the UK my entire life. As we approach this November, it’s vital that we reject hate speech, misinformation and online negativity.”
Former Suits actress Meghan, 39, described the November election as “the most important election of our lifetime”.
“When we vote, our values are put into action, and our voices are heard,” she said.
“Your voice is a reminder that you matter. Because you do and you deserve to be heard.”
Neither Harry or Meghan mentioned Mr Trump or his political rival Mr Biden by name, but some have interpreted their comments as critical of the president.
The Royal Family traditionally does not vote in the UK’s elections to demonstrate neutrality.
Meghan and Harry recently moved to California after making the shock announcement they were quitting royal duties and moving to North America, claiming they had endured unbearable intrusion and racist attitudes from the British media.
Mr Trump has met The Queen three times as president, including a visit to Windsor Castle in July 2018.
Earlier this year, he tweeted that Prince Harry would not receive taxpayer-funded security in the US after ditching his royal duties.
Mr Trump tweeted in March: “I am a great friend and admirer of the Queen & the United Kingdom.
“It was reported that Harry and Meghan, who left the Kingdom, would reside permanently in Canada. Now they have left Canada for the U.S. however, the US will not pay for their security protection. They must pay!”
Buckingham Palace appeared to distance itself from the recent comments made by Harry and Meghan.
The Palace highlighted the fact that the duke is no longer a working royal, and said his remarks were made in a “personal capacity”.
A palace spokesman said: “We would not comment.
“The duke is not a working member of the royal family and any comments he makes are made in a personal capacity.”