(CNN) Princes William and Harry have denied a UK newspaper story alleging that a rift in the royal family was caused by William's "bullying attitude."

In a joint statement sent to CNN, spokespeople for the Duke of Sussex and the Duke of Cambridge 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 statement said.

It followed a story in the Times of London on Monday, reporting that the Duke and Duchess of Sussex , Meghan and Harry, felt "pushed away" by William's "bullying attitude."

The article suggested the brothers "fell out because William wasn't friendly towards Meghan" and that the Sussexes were "constantly being bullied."