In a statement, Andrew, the Duke of York, said that "a number of stories" had been published over the past few weeks "that have no basis of fact".

He added that "the most recent, relating to my daughters, requires correction to terminate further speculation and innuendo".

The Duke said that suggestions he had asked for future husbands of Princesses Beatrice, 28, and Eugenie, 26, to have titles were "a complete fabrication".

"There is no truth to the story that there could be a split between the Prince of Wales and I over my daughters' participation as member of the Royal Family and any continued speculation is pointless."

According to reports, Andrew, 56, fears that any children the princesses may have will be "commoners", prompting efforts to improve their status by persuading the Queen and heir to the throne Charles to let their future husbands have earldoms.

But the Duke said he only wished for his daughters to "be modern working young women, who happen to be members of the Royal Family".

He added: "Whilst I appreciate, as granddaughters of The Queen, there is considerable interest in my daughters, I cannot continue to stand by and have the media speculate on their futures based on my purported interventions, which are completely made up and an invention."

The Duke's statement came on the same day that the princesses' mother, the Duchess of York, pleaded with the media to "stop bullying the York family".

She spoke as the two young women became patrons of the Teenage Cancer Trust, calling their "hard work" an example of "good parenting".

She said: "Both the Duke and myself, we could not be more proud of this moment because these are two girls that work so hard in their own careers, have taken time off today to spread the word of teen cancer, which is so important, and then go back to work.

"Let's focus more on this and less on title-tattle gossip."