Buckingham Palace issued a condemnation pictures showing the Duchess of Cambridge topless and rubbing sun-cream on Prince William.
The pictures were taken at an isolated chateux in the south of France using a long lens camera.
French Closer magazine ignited the storm by publishing the images, which UK newspapers had turned down.
Royal aides and lawyers are in talks about taking possible legal action.
Prince William and Kate Middleton, the Duchess of Cambridge, are currently on an official tour of the Far East.
The photos scandal will not be allowed to derail the trip - during which Kate delivered her first speech, about hospices for terminally ill patients.
A royal spokesman condemned the images:
"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," he said.
"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."
"The Duke and Duchess remain focused currently on their Tour of Singapore, Malaysia, Solomon Islands and Tuvalu on behalf of HM The Queen."