The Duke of Cambridge made no response when he was asked whether he backed his uncle the Duke of York.
Second in line to the throne William was leaving the Foundling Museum in London with the Duchess of Cambridge when a member of a TV news crew asked: “Do you support Prince Andrew?”
The duke leaned closer to hear but then walked past without commenting.
Andrew stopped using his HRH style and was stripped of his prestigious honorary military roles by the Queen less than a week ago.
William and the Prince of Wales would have been involved in the crisis talks to decide the duke’s future, ahead of Andrew being summoned to Windsor Castle to learn of his fate.
Andrew is facing a civil sexual assault case in the US, but denies the allegations.
The monarchy is seeking to distance itself from the ninth in line to the throne as the institution gears up for the Queen’s historic Platinum Jubilee this year.
On Friday, Charles refused to answer questions about the duke’s position while meeting people involved in the clear-up operation after Storm Arwen in the north east of Scotland.
Virginia Giuffre is suing Andrew for allegedly sexually assaulting her when she was a teenager.
She claims she was trafficked by the duke’s friend, convicted paedophile Jeffrey Epstein, to have sex with Andrew three times when she was 17 and a minor under US law.