The photos ran in the Friday edition under the headline "Heir it is!"
Royal officials had contacted the British press complaints commission Wednesday to ask U.K. papers not to publish the pictures.
While the photos are being widely circulated around the world, newspapers in the U.K. steered clear, instead using photos of the prince on vacation wearing swimming trunks and a fedora hat. The Sun published a bizarre mock-up of one of the pictures on its front page Thursday using one of its own journalists to stand in for Harry.
In a video posted on The Sun's website, managing editor David Dinsmore explained the reasons behind the decision to run the photos.
"This is about the ludicrous situation where a picture can be seen by hundreds of millions of people around the world on the internet, but can't be seen in the nation's favourite paper read by eight million people every day," he said.
"We are not against him letting his hair down once in a while. For us this is about the freedom of the press."
St. James's Palace, where Prince William and Prince Harry's staff work, said it had heard that a number of U.K. papers were thinking of using the pictures, the BBC reported. The palace said it would view the publication of the photos as an unacceptable invasion of privacy.
A letter to the watchdog from royal law firm Harbottle and Lewis warned that royal officials "entirely reserve their rights as to any future steps that they may take should publication take place."
According to the Guardian, the watchdog said it was "happy to pass on St James's Palace's view that publication" would amount to a violation of clause three of the complaint commission's editors' code of practice.
That clause says "it is unacceptable to photograph individuals in private places without their consent."
Any paper that ran the photos of Prince Harry naked risks being chastised by the commission, which can demand a newspaper publish an apology, but has no power to issue fines.
A newspaper could also potentially be open to an invasion-of-privacy lawsuit from the prince.
Two pictures of the naked 27-year-old prince were published Wednesday on the website of TMZ.com, a U.S.-based entertainment website.
Both pictures appear to show the third in line to the throne cavorting with a young woman, also naked. The website said the incident took place last weekend in a Las Vegas hotel suite following a game of strip billiards. It's not clear who took the pictures or if the prince knew they were being taken.
Leveson inquiry impact
Several past and present British news editors said the reluctance of even the famously bold British tabloids to show the pictures was undoubtedly due to the shadow imposed by the Leveson inquiry, which is looking into U.K. media ethics in the wake of the phone-hacking scandals that rocked the now-defunct News of the World tabloid.
"Literally any journalist worth his salt, whether at one end of the market or the other, would have said: 'Thank you God,'" former Sun editor Kelvin MacKenzie told BBC Newsnight in describing the level of interest surrounding the pictures.
"It doesn't affect Prince Harry at all. He is single and he is cavorting with ladies who wish to be cavorted with," he said. "So where are the issues? There are no issues except one: Leveson."
The Leveson inquiry is to release its report this fall and is expected to address the contentious issue of media regulation.
Prince Harry is now believed to be back in the U.K.