The snapshots were taken last week by French magazine, Voici, while the Clooneys were relaxing at their Lake Como, Italy, property.
In a statement, the Oscar-winning actor said the photos were taken illegally.
“Over the last week, photographers from Voici magazine scaled our fence, climbed our tree and illegally took pictures of our infants inside our home,” he said. “Make no mistake, the photographers, the agency and the magazine will be prosecuted to the full extent of the law. The safety of our children demands it.”
Voici defended itself with a statement of its own, saying they were serving the public’s interest.
“The images published in Voici this Friday are a response to a public demand. People love George Clooney and have been following his life story for years now. Those pictures do not put in danger Mr. Clooney, his wife or their kids.”
Amal Clooney gave birth to her twins, Ella and Alexander, a month and a half ago in England.