The Duke and Duchess of Cambridge are hugely saddened over the "grotesque and unjustifiable invasion of privacy" by a magazine which published topless photos of Kate, a royal spokesman says.
French publication Closer printed the pictures of the duchess, taken during their private holiday in France.
The royals are now considering legal action over the case.
Closer's editor says the couple were "visible from the street" and the images are "not in the least shocking".
The BBC's Nicholas Witchell said that the royals were "incredulous that any magazine would have felt they had a justification in publishing these pictures".
"They could go to law or seek a remedy through the French court - that is a big step to take but that is clearly what is being considered now," he said.
"I have rarely heard quite such a level of publicly expressed anger that I have heard today reflecting William's feelings.
"He is absolutely determined to protect the privacy of his wife; he has always been very protective of her and that anger has mounted during the day."
Our correspondent said that the prince had a "look of absolute thunder" on his face as they left Kuala Lumpur - a stop on their nine-day tour of South East Asia - to travel to Sabah in north Borneo.
Kate, meanwhile, "looked composed and was smiling", he said.
Closer editor Laurence Pieau said: "These photos are not in the least shocking. They show a young woman sunbathing topless, like the millions of women you see on beaches."
She described the reaction as "a little disproportionate".
"What we saw in the pictures was a young couple that have just got married, who are in love, who are beautiful. She's a princess of the 21st Century," said Pieau.
"They [the couple] are on the terrace of a mansion in the south of France which is not far from a road along which cars pass without any problem. They are visible from the street."
The photos look blurry, the BBC's Paris bureau said. There are four pages of photos of the couple, with Kate topless in several.
On the magazine's website, it says the pictures are of the couple "like you have never seen them before. Gone are the fixed smiles and the demure dresses. On holiday Kate forgets everything."
The duke and duchess, who were staying at the French chateau of the Queen's nephew, Lord Linley, "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", a spokesman for Clarence House, the Prince of Wales's office, 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 prime minister's official spokesman said: "The view from Downing Street is that they are entitled to their privacy."
The royal couple were told about the magazine's plan to publish the photos during breakfast in Kuala Lumpur, Malaysia, on their tour to mark the Queen's Diamond Jubilee. They are now on their way to north Borneo, where they are due to visit a rainforest.
It has emerged that British newspapers were offered photographs last week but turned them down.
The Sun's editor Dominic Mohan said the newspaper had no intention of breaching the couple's privacy by publishing what he described as "intrusive" pictures.
"The circumstances are very different to those relating to the photos of Prince Harry in Las Vegas. As we said at the time, he was at a party in a hotel suite with a large group of strangers and one of those present released a photograph into the public domain," he said.
The Sun was the only British newspaper to print the naked pictures of Prince Harry, defying a warning by Clarence House that they breached his privacy.
The Press Complaints Commission said it received hundreds of complaints from members of the public but did not act because it had not been contacted by representatives of the prince.
Lloyd Embley, editor of the Mirror and Sunday Mirror, said the papers were offered a set of pictures of the duchess in her bikini a week ago but, as with the pictures of Harry, they took the decision not to publish them.
In both cases they believed it would be a clear breach of the editors' code of practice involving breach of privacy.
Closer is not run by the same company as the British title; it is administered by Italian business Mondadori, owned by former president Silvio Berlusconi's holding company Fininvest.
A statement from the UK magazine said: "We were not offered any pictures of this nature and have no intention of publishing the photographs of the Duchess of Cambridge which have been published this morning."