The Duke of Cambridge also revealed that he had not yet spoken to his brother since the interview, but said he “will do”.
Harry told Winfrey the brothers’ relationship was now one of “space” but he hoped that time “heals all things”.
Sources quoted by The Mirror said William and Harry, despite having not spoken for months, were prepared to “put on a united front” later this year when a statue of their mother Diana is due to be unveiled at Kensington Palace on 1 July.
One source told the newspaper “tensions” between the brothers were “undoubtedly running high” but they understood the importance of putting “any differences aside for the ceremony”.
Watch: Prince William says Royals are 'very much not a racist family'
William and the Duchess of Cambridge were seen in public for the first time since the interview on Thursday during a visit to a school in east London to mark the return of children to classrooms this week and to support a youth mental health service.
When asked by a reporter if he had spoken to Harry since the interview, William replied: “I haven’t spoken to him yet, but I will do.”
He was then asked if the royal family were racist, to which he said: “We’re very much not a racist family.”
It comes after Harry and Meghan told Winfrey there had been “concerns” expressed by a member of the family over what colour Archie’s skin would be when he was born.
Buckingham Palace issued a statement on the Queen’s behalf on Tuesday that said the royal family was sad to learn the “full extent of how challenging the last few years have been for Harry and Meghan”.
It continued: “The issues raised, particularly that of race, are concerning. While some recollections may vary, they are taken very seriously and will be addressed by the family privately.”
Watch: The key revelations from Meghan and Harry’s Oprah interview