NEW: Irish Daily Star is conducting investigation before deciding whether to shut down
Catherine and Prince William "welcome" the injunction, the palace says
A court orders Closer magazine to hand over the photos within 24 hours
The royals have also filed a criminal complaint in France
Closer was fined Tuesday for publishing the topless photographs, and ordered not to distribute the magazine in print or online.
The court ordered Closer magazine to hand over the original photos to the royal family within 24 hours of the ruling and to pay them 2,000 euros (about $2,600).
The magazine must pay a further 10,000 euros a day if it is late in handing over the photos.
A French prosecutor opened a preliminary criminal investigation into the incident, the Nanterre prosecutor’s office said Tuesday.
Catherine and her husband, Prince William, the second in line to the throne, “welcome the injunction that’s been granted. They always believed the law was broken and that they were entitled to their privacy,” the palace said.
French law provides for “draconian sanctions” to protect against invasions of privacy, British lawyer Charlotte Harris said, including orders to take magazines off shelves and the imposition of serious fines.
Separately, the board of a newspaper that published the topless photos is conducting an internal investigation. The board of the Irish Daily Star was considering shutting down the newspaper but decided to await the investigation results, which are expected in “a few weeks.”
After the Irish Daily Star published the photos Saturday, one of the newspaper’s editors was suspended, pending the investigation.
The royal family filed a criminal complaint seeking invasion of privacy charges against Closer and possibly the photographer, a palace spokeswoman said.
The photos of Catherine sunbathing are more about invasion of privacy rather than nudity, royal biographer Christopher Andersen said.
Prince William and his brother, Prince Harry, still blame the media for the 1997 death of their mother, Princess Diana, in a Paris traffic accident as her driver fled paparazzi, Andersen said. French investigators concluded the driver of the car Diana was traveling in lost control while he was intoxicated.
The royal family is concerned about similar invasions, particularly if William and Catherine have a child, Andersen said.
In a civil court proceeding Monday in Paris, attorneys for the royals asked for damages and a court order to prevent the photos from being published again.
They also want existing photos taken offline, a palace spokesman said.
The court ruled in their favor on both counts Tuesday.
Lawyer Aurelien Hamelle denounced the published photos in court Monday, calling them an infringement of privacy, CNN affiliates reported.
“It is a scene of married life, intimate, personal, that has nothing to do on a magazine,” Hamelle said.
Chi, an Italian magazine owned by the same company as Closer, put out a special edition Monday with 26 pages of photos of William and Catherine on vacation.
As editors at Closer did last week, Chi executives defended publishing the photos despite the furor from London.
“It is a story worth publishing in an extraordinary edition because it shows in a natural light the everyday life of a very famous contemporary young couple in love,” Editor-in-Chief Alfonso Signorini said in a statement.
Chi and Closer are owned by the Mondadori publishing company, which is headed by Marina Berlusconi, daughter of former Italian Prime Minister Silvio Berlusconi.
CNN’s Per Nyberg, Laura Smith-Spark and Hada Messia, and journalist Peter Taggart contributed to this report.