The young British royals, who are currently in Malaysia, were consulting lawyers over what they called a "grotesque" breach of privacy by the French version of Closer magazine, palace officials said.
But the editor of the magazine said the photographs of the Duchess of Cambridge were "not in the least shocking".
The grainy pictures show Catherine, 30, wearing just the bottoms of a black and white bikini and having suncream rubbed on to her behind by William while on holiday in the south of France.
"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," their office St James's Palace 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."
The statement said officials acting on behalf of the couple "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" to mark the diamond jubilee of William's grandmother Queen Elizabeth II, it said.
Royal aides told AFP that William, the second in line to the British throne, and Catherine felt "anger and disbelief" and believed that a "red line has been crossed" by the publication of the photographs.
The incident "turns the clock back 15 years," one source said, referring to the intense media attention on Diana, Princess of Wales, who died in a car crash while fleeing paparazzi in Paris in 1997.
British Prime Minister David Cameron's spokesman said the royal couple were "entitled to their privacy." A source close to Cameron said he "echoes the sadness of the palace" over the publication of the photographs.
The pictures are a further headache for the royal family, already reeling from the publication last month of nude photos of William's younger brother Harry in a Las Vegas hotel.
Laurence Pieau, the editor of the magazine, defended the decision to publish the pictures.
"These photos are not in the least shocking. They show a young woman sunbathing topless, like the millions of women you see on beaches," Pieau told AFP.
In one of the pictures, the couple are laughing as they lounge in chairs near a folded red parasol. In another, Catherine holds the top of her bikini across her chest, either taking it off or putting it back on.
Closer magazine said the snaps were taken on the terrace of the Autet Chateau in Provence, southern France, where William and Catherine were said to have spent time last week before leaving for southeast Asia and the Pacific.
The magazine said the chateau is owned by Viscount Linley, the son of the queen's late sister Princess Margaret.
The three-day holiday began at Marseille-Marignane airport on September 5 and "Kate even smoked a cigarette between the airport's exit and the car that was to take them toward their little paradise," the magazine wrote.
Comparing the pictures to those of Harry cavorting naked with a mystery woman as he played strip billiards in Las Vegas, the magazine said: "Here there is no question of alcohol, of strip billiards or compromising positions, but simply a spouse at ease with her body, who has nothing to hide from her husband.
"Moments of grace, of complicity. Of love in its purest. Images of cloudless happiness."
British newspapers reportedly turned down offers to buy the pictures.
The row threatened to overshadow the royal couple's nine-day visit to Asia, which was meant to help introduce the pair overseas after their pomp-filled marriage last year.