Meghan and Harry's tell-all TV interview with Oprah Winfrey has plunged the monarchy into its biggest crisis since the 1997 death of Harry's mother Diana.
In the two-hour show, Meghan accused the royal family of raising concerns about how dark their son Archie's skin might be and ignoring her pleas for help while she felt suicidal.
Harry also said his father, Prince Charles, had let him down and that he had felt trapped in his royal life.
"The whole family is saddened to learn the full extent of how challenging the last few years have been for Harry and Meghan," Buckingham Palace said in a statement issued on behalf of Elizabeth.
"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."
The Palace considered this was a family matter, a royal source said, adding the royals should be given the opportunity to discuss the issues raised privately as a family.
The interview was watched by 12.4 million viewers in Britain and 17.1 million in the United States, triggering a crisis to which the monarchy had to respond, media said.
Earlier on Tuesday, Charles made no comment when asked by a reporter what he thought of the interview while visiting a COVID-19 vaccine pop-up clinic in London.
A royal source had the Queen, 94, who has been on the throne for 69 years, wanted to take some time before the Palace issued a response, saying it needed careful consideration.
A former senior royal aide said it was likely that the three most senior royals - the Queen, Charles and Prince William, would have held meetings with their private secretaries and communications chiefs to decide on their response.
"This is pretty important and they've got to judge it right," said the former aide, adding the Queen would have had the final say.