Legal analysts suggest the company hopes to recoup any legal costs and fines it may incur by increasing sales, thanks to the revealing pictures.
The grainy pictures published by Closer in France appear to have been taken with a long camera lens while the couple was staying at a private chateau belonging to William's uncle in Provence, in southern France.
The new privacy controversies have dredged up the royal family's often rocky relationship with the press and put a spotlight on how the palace deals with the media after the tragic death of William's mother, Diana, as she fled photographers in Paris 15 years ago.
William and Catherine were "hugely saddened to learn that a French publication and a photographer have invaded their privacy in such a grotesque and totally unjustifiable manner," a St. James's Palace spokesman said Friday.
"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 palace spokesman said.
"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."
Laurence Pieau, editor-in-chief of Closer in France, defended the decision to publish the images in an interview with CNN affiliate BFM-TV, saying: "We were just doing our job."
Pieau said that there had been no debate at the magazine over whether to publish the photos, and that they show the royals "are just like any other couple in love."
The website of Closer on Friday showed the front cover of the magazine with blurry images of William and Kate, along with the headline "Oh My God!" but did not link to the four-page spread.
But by Saturday that was replaced by a statement from the management of Closer, which said the photos it chose to publish "are in no case degrading."
"They show a young couple on vacation, beautiful, in love and modern, in their normal life. The article recounts the time the couple recently spent in southern France," it said. It also made clear the magazine is not linked with the UK publication of the same name.
William and his wife were in Malaysia when the news broke, part way through a nine-day Southeast Asian tour of Commonwealth nations, which started in Singapore and will conclude with a stop in Tuvalu.
The Asia tour forms part of diamond jubilee celebrations for the queen, William's grandmother.
British lawyer Charlotte Harris said Friday that Closer's decision to publish was a clear breach of French legal codes and was out of line with current views on people's right to privacy.
"The perception of the French was that they are less aggressive, that they have a culturally different opinion of where privacy laws should lie. Here they appear to have gone right over the other way," she said.
French law provides for "draconian sanctions" to protect against this kind of behavior, she said, including orders to take magazines off shelves and the imposition of serious fines.
But even if distribution of the images is contained to a degree, Harris said, the damage is done to the extent that very private information about the duchess has now become public knowledge.
No UK newspaper has so far published the photographs of Catherine.
In the case of Prince Harry, the photographs were widely circulated online but were published in only one UK tabloid, The Sun, after palace officials asked UK media not to run them.
The Sun has made clear that it won't publish the pictures of Catherine, however. Editor Dominic Mohan tweeted: "The Sun has no intention of breaching the royal couple's privacy. The circumstances are very different to those relating to the photos of Prince Harry in Las Vegas."
The Press Complaints Commission, the UK press watchdog, received about 3,800 complaints from the public over the Prince Harry photos but said it was inappropriate for it to take any action in the absence of a formal complaint from the palace.
Royal officials appear to be taking publication of the photographs of William and Catherine much more seriously.
The British media is currently under close scrutiny after revelations of phone hacking and other abuses. The conclusions of an independent judge-led inquiry, which may recommend greater restrictions on media freedoms, are expected by the end of the year.