Video report by ITV News Royal Editor Chris Ship
The Duke of Cambridge made the comments on camera on Thursday morning during a visit to an east London school.
He is the first member of the Royal Family to publicly address the race row sparked by Prince Harry and Meghan Markle's interview with Oprah Winfrey.
In the interview, the couple claimed that concerns were raised by a Royal Family member about Archie's skin colour before he was born. Oprah clarified the family member was not the Queen nor the Duke of Edinburgh.
When asked whether he had spoken to his brother since the bombshell interview, Prince William said: "No, I haven't spoken to him yet but I will do."
The Duke and Duchess of Cambridge were visiting in Stratford, London, to thank teachers involved in reopening after the lockdown.
ITV News Royal Editor Chris Ship said Prince Williams remarks were "unprecedented for a senior Royal to speak in this way" and that it "shows the fight they now have on their hands to repair their reputation following Meghan and Harry’s explosive claims".
After the interview aired on ITV on Monday night, Buckingham Palace released a statement on Tuesday, saying the race allegations raised "are concerning".
In a statement issued on behalf of the Queen, it said the issues would be "addressed by the family privately".
"The whole family is saddened to learn the full extent of how challenging the last few years have been for Harry and Meghan," the statement said.
"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."
Before the palace's response, Prince Charles was asked whether he watched the interview as he visited a pop-up vaccine clinic in north London on Tuesday.
The Prince of Wales did not reply and continued to walk with his entourage to the next part of the tour.
The claim that a Royal Family was concerned about Archie's skin colour has triggered a country-wide debate on issues surrounding race and ethnicity.
Barbados has reacted by deciding to dispense with the Queen as head of state.
Speaking on Tuesday, Meghan's estranged father Thomas Markle dismissed suggestions of racism in the royal family, telling ITV's Good Morning Britain it was "bull****" and he did not "think the British royal family are racist at all".
The 76-year-old said: "The thing about what colour will the baby be, or how dark will the baby be, I'm hoping it's just a dumb question from somebody, it could be that simple.
"It could be somebody's just asked a stupid question, rather than someone being racist."
Harry and Meghan's interview with Oprah first aired in the US on Sunday night. It was broadcast to UK viewers on ITV on Monday night. People in the UK can still watch the interview on ITV Hub.