"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 members of the royal family and any continued speculation is pointless."
Rather than wanting more public roles for the Princesses, he said he wanted them to be "modern working young women who happen to be members of the royal family".
His intervention came just hours after his former wife, Sarah, made a public plea to "stop bullying the York family".
As her daughters became patrons of the Teenage Cancer Trust, she called their "hard work" an example of "good parenting".
The Duchess of York and the two princesses visited a specialist teen cancer unit in London to mark the occasion, meeting young people with the disease.
The Duchess 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."
She went on: "Let's focus more on this and less on tittle-tattle gossip. Stop bullying the York family, please."
It comes after singer Ed Sheeran disclosed that Beatrice slashed his cheek with a ceremonial sword as she pretended to knight singer James Blunt at a dinner party.
Both princesses have faced criticism over their fondness for holidays: in 15 months, Eugenie took eight holidays, from Burma to California.
In the year to December 2015, Beatrice managed 18 trips, to places including the Caribbean, Verbier, Abu Dhabi, Rome, Ibiza and Florida.
