Prince Charles "feels enormously let down" by the claims made during the interview.
It comes as:
A source close to the royal household said: "The prince believes in diversity and his actions show that.
"He was the first person to highlight the Windrush generation and the contributions they made to British society.
"He has worked hard for the Muslim community.
"Of all the members of the royal family, he has taken this issue the most seriously."
A palace source was also reported to have said that Charles had had a "complicated relationship" with William and Harry and that it was "not a straightforward" father and son relationship.
The fallout from the Oprah chat is still unfolding after Meghan and Harry made a series of explosive claims about their lives as royals - although The Sun exclusively reported today the Queen is "sad, not angry".
Meghan said Kate Middleton received preferential treatment and made her cry during an argument over flower girl dresses.
Meghan and Harry alleged a senior royal made racism comments before the birth of Archie Credit: PA The couple haven't named the person responsible for the comments, but say it wasn't the Queen or Prince Philip Credit: CBS The source also claims Charles has a 'complicated relationship' with both of his sons Credit: Getty Meanwhile, Harry claimed William and Charles are “trapped” by their royal responsibilities.
The princes have barely spoken to each other for more than a year after Harry and Meghan “blindsided” the Queen and announced Megxit on their Sussex Royal Instagram page.
William became the first royal to publicly hit back over the racism allegations.
Last Thursday, as he visited a school for an engagement, he told reporters the royals are "very much not a racist family".
But since then, Meghan and Harry have faced further claims they're leaking details of their private lives to the press.
It came after Meghan's pal Gayle King revealed Harry has spoken to Charles and William for the first time since the interview aired - but talks were "unproductive".
She told CBS This Morning: "Well, I did actually call them to see how they are feeling, it's true, Harry has talked to his brother and his father, too.
Meanwhile, Harry said William and Charles are 'trapped' in their roles Credit: Goff The fallout from the chat is still unfolding, although a source told the Sun the Queen is 'sad rather than angry' Credit: AP "The word I was given was, those conversations were not productive. But they are glad they at least started a conversation."
The breakfast show host also suggested that Meghan was unhappy no one in the Royal Family had thought to telephone her.
After the interview aired, the palace released a statement voicing "concern" over the issues raised, "particularly that of race".
However, the statement added that "some recollections may vary".
A royal insider told The Sun the Queen has been left saddened by the claims made.
"She is not angry, she is just sad," they said.
"They have always worried about him (Harry) and the Queen feels very protective about him.
"They always tried to support him when Meghan came along.
"They all worried less about him when Meghan was on the scene as he seemed so happy."
Charles has engaged in royal duties since - but has so far not commented in public on the claims made.
Prince Harry and William speak for first time since Oprah chat but talks were 'unproductive', Meghan Markle's pal claims