William and Harry spoke out on the day the Queen called a summit at Sandringham for senior royals to discuss face to face for the first time the Sussexes' bombshell plans to forge a new role for themselves.
The statement did not name the newspaper but the Times has a front page story about the crisis, and says a source told the publication that Harry and Meghan "regarded themselves as having been pushed away by what they saw as a bullying attitude from the Duke of Cambridge".
The report goes on to say that these allegations have been contested by other sources close to the Cambridges and Harry.
A joint statement issued on behalf of the princes 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."
There has been much speculation about the relationship of the brothers who a few years ago were working closely together on charitable projects and lived metres from each other at Kensington Palace.
But Harry has conceded how the siblings are moving in different directions and their relationship, although close, has come under real strain.
Harry and Meghan made clear in their statement last week they want to step back from being senior royals, become financially independent and split their time between North America and the UK.
In a documentary, filmed during the Sussexes tour of southern Africa last autumn, the duke said he and William were now "on different paths" and have "good days" and "bad days" in their relationship.
The decision to quickly deny the allegation of bullying reveals the brothers want to let the public know they may have their differences but behind the scenes things are amicable.