Prince Edward, 61, was the first senior royal to speak on the issue, telling reporters during an official trip to Dubai that it was important to “remember who the victims are in all of this”.
In a rare move on Monday, King Charles issued a strongly worded statement addressing the situation.
According to Buckingham Palace, His Majesty pledged to “stand ready to support” police following the launch of an investigation into the former Duke of York’s conduct.
“The King has made clear, in words and through unprecedented actions, his profound concern at allegations which continue to come to light in respect of Mr Mountbatten-Windsor’s conduct,” a spokesman said.
Andrew Mountbatten-Windsor has not commented on the latest accusations. He has previously denied any wrongdoing.