Lawyers were being consulted by royal aides after the images showing the future Queen wearing just a pair of bikini bottoms were published in the French magazine Closer.
William and Kate were said to be feeling "anger and disbelief" at the publication of the photographs, taken while on a private holiday.
The St James's Palace statement said: "Their Royal Highnesses have been hugely saddened to learn that a French publication and a photographer have invaded their privacy in such a grotesque and totally unjustifiable manner.
"The incident is reminiscent of the worst excesses of the press and paparazzi during the life of Diana, Princess of Wales, and all the more upsetting to the Duke and Duchess for being so.
"Their Royal Highnesses had every expectation of privacy in the remote house. It is unthinkable that anyone should take such photographs, let alone publish them. Officials acting on behalf of their Royal Highnesses are consulting with lawyers to consider what options may be available to the Duke and Duchess."
William and Kate are midway through a Diamond Jubilee tour of the Far East, which had been going well but is now likely to be overshadowed by the controversy. The photographs were taken last week while the couple were staying in Provence at a chateau owned by Lord Linley, the Queen's nephew, ahead of their trip.
St James's Palace said the royal couple would not let the controversy distract them. A spokesman said: "The Duke and Duchess remain focused currently on their tour of Singapore, Malaysia, Solomon Islands and Tuvalu on behalf of HM the Queen."
Publishers of the UK edition of Closer distanced themselves from the French magazine. They said the two publications made "entirely independent editorial decisions", and pointed out that the French magazine is published by a separate, Italian company. The UK's Closer magazine said it had no intention of publishing the topless pictures and had not been offered them.