Video report by ITV News Royal Editor Chris Ship
In a statement, issued on behalf of the Queen, it said the issues would be "addressed by the family privately".
The statement reads: "The following statement is issued by Buckingham Palace on behalf of Her Majesty The Queen.
"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."
Does Buckingham Palace statement go far enough? Royal Editor Chris Ship has the answer
A series of claims were made during the nearly two hour long interview with US chat show host Oprah - the first of its kind since the couple left the UK and stepped back from Royal life.
Meghan also spoke openly about experiencing suicidal thoughts during her time in the Royal Family, revealing she got to the stage where she "just didn’t want to be alive anymore."
The statement is the first response from the Palace since the interview aired on US network CBS on Sunday, and on ITV on Monday night.
Since the broadcasts, many high-profile faces have publicly sided with the Palace or the Sussexes.
Tennis star Serena Williams and former Wales rugby player Gareth Thomas are among those who backed Harry and Meghan on social media, while Meghan's estranged father insisted that the Royal Family is not racist on Tuesday morning.
Hours before the Palace put out their statement on Tuesday, the Prince of Wales refused to say whether he'd watched the tell-all interview.On a visit to a pop-up vaccine clinic in north London, Charles was asked what he thought of the interview.
The prince didn't reply and continued to walk with his entourage to the next part of the tour.
The Sussexes have also remained largely silented since the interview, except from releasing a photo of their growing family.
The black and white image taken and shared by photographer Misan Harriman captures a smiling, pregnant Meghan stood by a tree cuddling Archie as Harry stands behind her, embracing his wife.
Oprah With Meghan and Harry is available to watch on demand on ITV Hub for viewers in the UK.
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