It was said that Prince Harry was feeling forced out of the royal family because of Prince William's "bullying attitude" towards he and wife Meghan, Duchess of Sussex.
However, the brothers have now hit back at the claims calling them "offensive" and "potentially harmful".
A spokesperson for the pair said: "Despite clear denials, a false story ran in a UK newspaper today speculating about the relationship between The Duke of Sussex and The Duke of Cambridge.
"For brothers who care so deeply about the issues surrounding mental health, the use of inflammatory language in this way is offensive and potentially harmful."
The use of inflammatory language in this way is offensive and potentially harmful.
The statement comes as Harry and William are due to attend a summit today at Sandringham with the Queen and Prince Charles to discuss Harry and Meghan's decision to step back from their roles as senior royals.
A source recently told The Sun: "The family will gather on Monday at Sandringham to talk things through. Attendees will be Her Majesty, the Prince of Wales, the Duke of Cambridge and the Duke of Sussex.
"Making a change to the working lives and the role in the monarchy for the Duke and Duchess of Sussex will require both complex and thoughtful discussions."
Last week, Meghan and Harry released a statement revealing their plans to take a step back from royal life.
They said they will work to become "financially independent" while still "fully supporting" the Queen.
At the time, Buckingham Palace officials later described the move as "complicated".
They said in a brief statement: "Discussions with The Duke and Duchess of Sussex are at an early stage.
"We understand their desire to take a different approach, but these are complicated issues that will take time to work through."
Meanwhile, it was recently reported that William told a friend he can't "put his arm around" his brother anymore.
He said, according to the Sunday Times newspaper: "I've put my arm around my brother all our lives and I can't do that anymore; we're separate entities. I'm sad about that.
"All we can do, and all I can do, is try and support them and hope that the time comes when we're all singing from the same page. I want everyone to play on the team."
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