Its website also showed an image of the front cover with the Duchess in a bikini apparently about to remove her top. The pictures were allegedly taken while Kate was on holiday with her husband, the Duke of Cambridge, in France last week.
The couple were staying in Provence at a chateau owned by Lord Linley, the Queen's nephew, ahead of their current Diamond Jubilee tour of south-east Asia and the South Pacific on behalf of the Queen.
Mail Online quoted a royal source as saying: "It is impossible to tell at this stage whether the photographs are genuine or indeed purport to show what the magazine claims, so we are having to wait and see what transpires."
But the newspaper said there could be little doubt of the magnitude of royal officials' anger and disgust if the pictures are published.
It would restart the row over privacy which raged around Prince Harry last month, when embarrassing images emerged of him frolicking naked in a Las Vegas hotel. Staying in a reported £5,000-a-night hotel suite, Harry was filmed wearing a hat, sunglasses and colourful swimming shorts, and socialising with bikini-clad women at a pool party.
The Sun was the only British newspaper to defy a Press Complaints Commission advisory note not to publish photos of Harry in the nude with an unnamed woman.
The Mail said that the pictures of the Duchess were clearly taken on private property using cameras with extremely long lenses, which means no British newspaper would publish them.
It said the timing of publication could not be worse, with the Cambridges almost midway though a hugely successful tour on behalf of the Queen to celebrate her Diamond Jubilee. They 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 which makes the timing even more difficult.
Duchess overcomes speech nerves
The Duchess of Cambridge confessed she was nervous about her first speech abroad when she addressed staff and supporters of a Malaysian hospice, praising the provision of care to the terminally ill.
When asked about her speech at a dinner thrown in honour of the Duke and Duchess's Diamond Jubilee tour, Kate replied: “I was so nervous and I am glad that it is over with.” Kate appeared relaxed and was in greater control of her nerves than her first public speech in March.
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