The Duke and Duchess of Cambridge have said the publication of photographs showing Kate topless on holiday is a "grotesque and unjustifiable" invasion of their privacy.French magazine Closer published the pictures today.
St James's Palace has confirmed the pictures are of Kate and in a statement said the royal couple are "saddened" by their publication.
The images show the Duchess topless on the terrace of a private house in France last week.
Prince William and Kate are said to have been "very angered" and believe a "red line has been crossed".
"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 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."
The palace said it is consulting French lawyers.
It added: "The Duke and Duchess remain focused currently on their Tour of Singapore, Malaysia, Solomon Islands and Tuvalu on behalf of HM The Queen."
The magazine's French website showed an image of its new front cover with a heavily pixellated photograph of the Duchess in a bikini apparently about to remove her top.
But the pictures were not pixellated in the magazine when it was published this morning.
The publication's editor, Laurence Pieau, wrote on her Twitter page on Thursday: "We can say that after tomorrow's Closer, Harry will feel less alone ..."
The pictures appear to have been shot using a long-lens camera from a distance and were allegedly taken while Kate and William were on holiday in France last week.
The Duke and Duchess were staying in Provence at a chateau owned by Lord Linley, the Queen's nephew.
William and Kate were told about the pictures before they visited the Assyakirin Mosque in Kuala Lumpur, Malaysia, and had also looked at the images on the website.
The couple are currently on a Diamond Jubilee tour of southeast Asia and the South Pacific on behalf of the Queen.
The palace said once they had a break in their schedule the couple would "turn their minds to what, if any, action they wish to take".
The French edition of Closer magazine is published by a different company to the British edition.
In a statement Closer magazine UK said it "would never publish topless images of a member of the Royal family on its cover or otherwise".
Sky sources at Trinity Mirror, publisher of the Daily Mirror and People newspapers, say they were offered different pictures of the Duchess of Cambridge while on holiday in France but not ones of her topless.
They turned the offer down.
During the visit to the mosque earlier Kate wore a head scarf as she and her husband were greeted by the Imam.
Following Islamic rules, the couple removed their footwear before being shown inside.
They listened to readings from the Koran and were told about practices of Islamic observance, including preparations for prayer and the role of the mosque in the community.
Kate appeared unfazed as news of the pictures spread around the world. If she had been embarrassed then it didn't show.
And later a relaxed Duchess smiled and waved at Malaysians who had gathered to see her at a park in central Kuala Lumpur.
She stopped, chatted and joked with her husband as they made their way on foot towards a conference centre where the Duke delivered his first speech in the country.
The couple have left the Malaysian mainland and have flown to Kota Kinabalu, capital of the state of Sabah on Borneo, for the next leg of their tour.
Publication of the images revives the privacy row prompted by photographs that emerged last month of Prince Harry frolicking naked at a Las Vegas hotel.
The Sun was the only British newspaper to defy a Press Complaints Commission advisory note not to publish photos of the prince naked with an unnamed woman.
The Duke and Duchess arrived in Singapore on Tuesday and are currently in Malaysia before travelling on to Borneo, then the South Pacific.
Malaysia is a largely Muslim country with laws on public decency, making the timing of the pictures' emergence even more difficult.