The Duke and Duchess of Sussex made the announcement on Wednesday that they intend to "step back" from being frontline royals, split their time between the UK and North America, and work towards becoming "financially independent".
The brothers spoke out to deny a “false” media report, which had alleged “bullying” by William, the Duke of Cambridge, to be among the factors behind the royal split.
"Despite clear denials, a false story ran in a UK newspaper today (Monday) speculating about the relationship between the Duke of Sussex and the Duke of Cambridge,” the joint statement notes.
"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," it notes.
While the statement does not name the UK newspaper or the specific report in question, it is believed to be referring to a story in ‘The Times' on Monday with the headline: Princes ‘fell out because William wasn't friendly towards Meghan'.
It alleges that Harry and Meghan felt “pushed away from the royal family by the ‘bullying' attitude” of Prince William.
The newspaper referred to a source close to Harry and Meghan as saying that Prince William had been insufficiently welcoming towards 38-year-old Meghan when she first started dating Harry and that the brothers' relationship suffered a blow due to that.
The report, however, admits that the analysis is contested by sources close to both Princes William, 37, and Harry, 35.
The statement comes ahead of a crucial Sandringham Summit at Queen Elizabeth II's Norfolk estate where the brothers are set to meet face-to-face alongside the 93-year-old monarch and their father, Prince Charles, for crisis talks over Harry and Meghan's future roles as semi-independent royals.
Prince William has previously spoken of his "sadness" at the broken bond with his younger brother and expressed the hope that they would “play on the team” again in the future.
The brothers were seen as being close until a split emerged months after Harry's wedding to Meghan, an American actress, in May 2017 when they decided to divide up their joint charitable foundation.
The rare joint statement indicates their unhappiness at the continuing UK media speculation over their relationship.