Mr Bashir spoke to Diana for an edition of BBC Panorama broadcast in 1995. However Earl Spencer, Diana’s brother, alleges the interview was only acquired through widespread deceit.
The BBC has promised a full investigation into the claims.
Mr Bashir, who is recovering from a heart operation and coronavirus, has yet to comment publicly.
The call for Prince Harry to comment publicly was made by the editor-in-chief of Majesty Magazine, Ingrid Seward.
Speaking to The Sun she said: “Harry’s silence speaks volumes.
“He is normally so keen on letting his opinions be known — why hasn’t he done so in this case and stood by his brother to share the responsibility.
“It is odd he hasn’t spoken out about the BBC and Bashir case as he has been speaking out a lot about other things recently.
“Harry should really man up and forget the fallout with his brother.”
During the 1995 interview Diana famously told Mr Bashir “there were three of us in this marriage”, referencing Camilla Parker-Bowles.
William’s intervention was welcomed by Ms Monckton, one of Diana’s closest friends.
Speaking to ITV News she said: “For [William] and for Kensington Palace to issue a statement, I think shows how deeply involved he has become in this story and about how his mother was treated.
“It’s very important that we look at it 25 years on.
“It did change the course of history.”
Diana married Prince Charles in 1981 with the service broadcast live to hundreds of millions around the world.
However the marriage broke down with accusations of adultery at both ends.
The couple divorced in 1996, one year before Diana was killed in a Paris car crash.