Meghan told Oprah Winfrey in their interview earlier this year that before the couple welcomed their son Archie, a member of the royal family had raised “concerns” with Harry about how dark their child's skin might be.
Former Good Morning Britain host Morgan has now hit out at the couple, saying that by refusing to name the person they are smearing the entire family.
Sharing a newspaper article claiming that Harry and Meghan did think about identifying the person, he tweeted: “Go on then, you gutless weasels - name the supposed Royal racist and let them respond.
"Otherwise you continue to smear the whole family."
Go on then, you gutless weasels - name the supposed Royal racist and let them respond. Otherwise you continue to smear the whole family.
— Piers Morgan (@piersmorgan) August 25, 2021
It is not the first time the TV star has been outspoken about Harry and Meghan.
He stepped down from Good Morning Britain in March after sparking a controversy when he said he did not believe things Meghan said in her sit-down with Oprah.
And he has continued to be critical of the pair.
Earlier this summer he had a pop at Harry after the prince likened his royal life to 1998 film The Truman Show, which sees Jim Carrey play a man under constant scrutiny as the unwitting star of a reality show.
“For a guy who craves privacy, Prince Harry sure is yapping a lot about his private life...” Morgan tweeted.
Morgan dubbed the Duke and Duchess of Sussex "Prince Poison and Princess Pinocchio" in the rant, which was in response to the news that Harry is to publish a tell-all memoir next year.
Watch: Piers Morgan warns of the effects of long COVID