The race issues raised by the Duke and Duchess of Sussex are “concerning” and will be addressed by the family privately, Buckingham Palace has said.
In a statement, the Palace said “recollections may vary” but the claims made in their interview with Oprah Winfrey were “taken very seriously”.
Meghan told Winfrey Harry had been asked by an unnamed family member “how dark” their son Archie’s skin might be.
The Palace said the Sussexes would “always be much loved family members”.
The response from Buckingham Palace came after crisis meetings involving senior royals.
Pressure had been growing to respond to the interview in which Meghan – the first mixed-race member of the modern Royal Family – revealed the comments about their son’s skin colour.
Prince Harry later clarified to Winfrey that the comments were not made by either the Queen or the Duke of Edinburgh.
The statement, which came a day and a half after the interview was first broadcast in the US, said: “The whole family is saddened to learn the full extent of how challenging the last few years have been for Harry and Meghan.
“The issues raised, particularly that of race, are concerning. Whilst some recollections may vary, they are taken very seriously and will be addressed by the family privately.”
During a visit in London earlier, Prince Charles did not speak about the interview, in which the Sussexes addressed deeply personal topics of racism, mental health, the media and other members of the Royal Family.
The UK broadcast on Monday night was watched by an average of 11.1 million people.
In it, the duchess said there had been times when she “didn’t want to be alive any more” because she found royal life so difficult. She said she asked for help from the Palace but received none.
Meghan said conversations about how dark Archie’s skin might be when he was born took place “in tandem” with discussions about why he would not be given a royal title and police protection.
Under rules in place since 1917, the couple’s children would not automatically become princes or princesses – unless the Queen was to intervene.
Asked by Oprah whether there were concerns that her child would be “too brown” and that would be a problem, Meghan said: “If that is the assumption you are making, that is a pretty safe one.”
But the couple have refused to say which family member made the comments. That conversation, I am never going to share,” said Prince Harry. “At the time it was awkward, I was a bit shocked.”
Harry also said it hurt that no one in his family ever spoke out in support of Meghan after news headlines and articles with “colonial undertones”.
Labour leader Sir Keir Starmer said Meghan’s allegations about racism and a lack of mental health support should be taken “very seriously”.
Downing Street said Prime Minister Boris Johnson had watched the interview on Monday night, but declined to comment further.