The three Royal households - Buckingham Palace, Clarence House and Kensington Palace - released a joint statement following claims in The Times newspaper of a "power struggle" involving Sir Christopher Geidt, the long-serving private secretary to the Queen.
It was confirmed in the summer that Sir Christopher, whose role is to act as the channel of communications between the Queen and Downing Street, was due to step down next month after a decade's service.
But unnamed sources said his departure was hastened following complaints from Charles and the Duke of York about the transition of power from the Queen and the heir apparent.
In the statement, the Royal households said: "While we never comment on the confidential employment details of individuals, it was previously announced in July that Sir Christopher Geidt is stepping down after 10 years as private secretary.
"At the time of the announcement, the Lord Chamberlain (the Earl Peel, who is head of the Queen's household) paid tribute to the major contribution made by Sir Christopher who, in turn, commended the support offered to Her Majesty by other members of the Royal Family.
"Indeed, recent years have seen an ever-closer working relationship between all the different Royal Households and their respective teams.
"The Prince of Wales and the entire Royal Family are committed to supporting the Queen in whatever way they can at Her Majesty's request.
"Beyond that, we are not going to engage with a story based on rumours from unnamed sources."
Sir Christopher, who also served as private secretary to the UN secretary general's special envoy to the Balkans, Carl Bildt, will be succeeded by the Queen's deputy private secretary Edward Young.
He was knighted under the Royal Victorian Order, for service to the monarchy, and was later made a knight commander of the Order of the Bath, for public service.