The palace has already launched a civil lawsuit against France's Closer magazine, which published the paparazzi snaps of Kate, the Duchess of Cambridge, relaxing during a holiday at a private villa in Provence.
The couple is hitting back hard against publication of the pictures, which William's office called a "grotesque" abuse of the young royals' privacy.
A spokeswoman for William's St. James's Palace office said the couple's lawyers would file a complaint with French prosecutors on Monday against the unidentified photographer or photographers involved.
"The complaint concerns the taking of photographs of the Duke and Duchess of Cambridge whilst on holiday and the publication of those photographs in breach of their privacy," she said on condition of anonymity in keeping with palace policy.
The palace said it would be up to French prosecutors to decide whether to investigate and pursue a criminal complaint for breach of privacy or trespassing.
The couple's lawyers are already due in a Paris court Monday seeking an injunction against Closer's publisher, the Italian media group Mondadori. It also publishes Italy's Chi gossip magazine, which says it will publish 26 pages of the images on Monday.
The palace will seek damages from the publisher, which is owned by former Italian Premier Silvio Berlusconi.
The palace said it was considering "all proportionate responses" against Chi, though no decision has been made on legal action against it or the Irish Daily Star which reproduced the Closer photos on Saturday.
No British publication has run the pictures, and Britain's tabloids have lined up to denounce them as an invasion of the duchess' privacy.
The strong response stands in contrast to the reception of naked photos of Prince Harry partying in Las Vegas, which appeared online last month and were later published in Britain's Sun tabloid. The palace shrugged off the photos, snapped during a game of strip billiards, and took no action against those who published them.
Some see British papers' reluctance to run the Kate photos as a sign that the country's once-rambunctious tabloids have been cowed by a scandal over phone hacking and other wrongdoing, which brought public opprobrium and an ongoing media-ethics inquiry.
The incident also has evoked memories of the paparazzi hounding of William's late mother, Princess Diana. A coroner's inquest found that pursuing photographers were partly responsible for her death in a Paris car crash in August 1997.
In bad news for the Irish Daily Star, both its owners criticized it for publishing the Kate photos.
British company Northern and Shell, which co-owns the tabloid with Ireland's Independent News and Media, or INM, said it was "profoundly dismayed" the Dublin newspaper had run the pictures. Its chief, Richard Desmond, said he planned to pull out of the joint venture that runs the tabloid.
Independent News and Media chief executive Joe Webb offered his "deepest apologies" and said the company would be "launching an internal inquiry to ensure there will never be a repeat of this breach of decency." But Webb said in a statement he hopes to preserve the Irish Daily Star and its 70 employees.
In Italy, the newspaper La Repubblica - a longtime foe of Silvio Berlusconi - criticized Chi's decision to publish the photos, saying they were incompatible with his status as politician and statesman.
Berlusconi's daughter Marina, who heads Mondadori, defended her father, saying he could not interfere with the publisher's "editorial autonomy."
La Repubblica said she had written to the newspaper asking rhetorically: "What should he have done? ... Should he have forced himself to not publish that which the overwhelming majority of gossip papers, in every part of the globe, would have competed with each other to have?"
The storm over the photos erupted as William and Kate made an official tour of Singapore, Malaysia and the South Pacific. They arrived in the Solomon Islands on Sunday and will end their trip Tuesday in the island nation of Tuvalu.
Associated Press Writer Frances D'Emilio in Rome contributed to this report.