Princes William and Harry on Monday put on a rare united front to dismiss a "false story" speculating about their relationship, as senior royals meet for talks about the younger brother's future.

Harry and his wife Meghan caught the institution off guard last week when they announced their intention to step back from frontline royal duties.

The 35-year-old former army officer has previously all but confirmed a rift with his older brother, prompting speculation as to the cause and that it may have influenced his decision to quit.

William and Harry, also known by their formal titles the Duke of Cambridge and Duke of Sussex, issued a rare joint statement to condemn one report, without specifying the publication.

"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," it said.

"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 Times cited an unnamed "insider" as saying Harry and Meghan felt they had been "pushed away by what they saw as a bullying attitude from the Duke of Cambridge".

But it also cautioned: "These claims have been strongly contested by sources close to the Cambridges, as well as some close to Prince Harry."