The race issues raised by the Duke and Duchess of Sussex in their interview with Oprah Winfrey are "concerning" and "taken very seriously", Buckingham Palace has said.
In a statement, the Palace said "recollections may vary" but the matters would be addressed privately.
Meghan told Oprah that 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.
The Palace had been under growing pressure to respond to the interview in which Meghan - the first mixed-race member of the modern Royal Family - said that before their son Archie was born, questions had been asked about his skin colour.
Prince Harry later clarified to Oprah that the comments were not made by either the Queen or the Duke of Edinburgh.
Figures from US TV network CBS suggest that nearly 50 million people around the world have watched Oprah's interview with the couple.
In other developments, Piers Morgan has stood by the comments that led to his departure from ITV's Good Morning Britain show - including that he did not "believe a word" of what Meghan said in the interview.
It is reported a formal complaint by the duchess has been lodged with ITV but neither representatives for the Sussexes nor ITV have confirmed this.
Chris Ship, the royal editor of ITV News, said in a tweet that it was believed Meghan had raised concerns about how Morgan's words "affect the issue of mental health and what it might do to others contemplating suicide".
The statement from the Palace, 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.
"Harry, Meghan and Archie will always be much loved family members."
It is understood the royals wanted to carefully consider their response and to give the British public an opportunity to watch the interview first, when it was broadcast on Monday evening.
They are said to consider this a family matter and to believe they should be given the opportunity to discuss the issues privately.
Downing Street has confirmed Prime Minister Boris Johnson has watched the interview, but his official spokesman declined to comment on the Palace's statement.
'A conciliatory tone with a gentle challenge'
Although likely, it was never absolutely certain that the Queen would issue a statement following the interview given by her grandson and his wife.
The risk was that any response would add to the "royals in crisis" narrative which is playing out across front pages and TV screens across the globe.
But having had time to discuss the claims made by Harry and Meghan, four short sentences convey the message from the Palace that this is a private family matter and the specific allegations will not be publicly addressed.
The tone is conciliatory, with reference to the Sussexes as much loved family members. There is a gentle challenge in the line "whilst some recollections may vary", but also an assurance that concerns will be taken seriously.
And we can be sure that - at least as far as the UK-based royals are concerned - any bridge-building will be done in private.
Meanwhile, the board of the Society of Editors has said it will "work towards being part of the solution" after coming under fire for its initial reaction to Meghan and Harry's interview.
It previously said it was "not acceptable" for the couple to make claims of racism in the press "without providing any supporting evidence".
But in a new statement the organisation said its earlier comments did not address that "there is a lot of work to be done in the media to improve diversity and inclusion".
"We will reflect on the reaction our statement prompted and work towards being part of the solution," it added.
It comes as MPs could push for a House of Commons debate to discuss possible actions following the media's "hounding" of Meghan.
Labour's Holly Lynch, who co-ordinated a letter from female MPs in support of Meghan in 2019, has questioned the way the press is regulated.
"How long do you continue to let that fail before you have to recognise it has failed and say 'what next?'" she said.
During a visit in London earlier, Prince Charles did not respond when he was asked if he had seen 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.
One of Meghan's close friends said she had been "worried, terrified, sad" to see the duchess's mental health problems.
Actress Janina Gavankar also told ITV's This Morning: "The family and the staff were well aware of the extent of it, and though their 'recollections may vary', ours don't, because we lived through it with them."
Gavankar, who watched the TV show air with both Meghan and Harry, added the couple were "feeling free" since the broadcast.
Meghan told Oprah that 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.
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