Buckingham Palace “will not want to feel rushed into saying something” about Prince Harry and Meghan’s claims.
The couple spoke about racism, mental health, the media and other members of the Royal Family in an interview.
Meghan’s father Thomas Markle has criticized the interview’s timing.
The duchess – who is the first mixed-race member of the modern Royal Family – said a low point came when Harry was asked by an unnamed royal family member “how dark” their son Archie’s skin might be.
Prince Harry later clarified to Oprah that the comments were not made by either the Queen or the Duke of Edinburgh.
Meanwhile, US President Joe Biden’s spokeswoman said he would praise anyone for having the courage to speak out about mental health.
White House press secretary Jen Psaki described Prince Harry, 36, and Meghan, 39, as “private citizens” who were “sharing their own story in their own struggles”.
An average of 11.1m people in the UK watched the two-hour interview when it was screened on ITV on Monday night after being broadcast in the US by CBS the previous day.