Kensington Palace, the official home of Prince William and his wife Kate, published a letter sent to media standards organizations, detailing recent incursions on the family's privacy.
It said photographers have hidden in car trunks, obscured themselves in sand dunes, monitored the movement of Prince George and his nanny around London parks and used other children to draw Prince George into view on playgrounds.
The palace says the increasing incursions present a risk "in a heightened security environment," and that a line has been crossed.
"The worry is that it will not always be possible to quickly distinguish between someone taking photos and someone intending to do more immediate harm," the palace said.
The royal couple have gone to great lengths to protect the privacy of their children, releasing only a handful of images of the children on special occasions. That policy, however, raises the value of paparazzi images, giving greater incentive to observe and photograph Prince George in particular, who is the primary target at the moment.
"Every parent would understand their deep unease at only learning they had been followed and watched days later when photographs emerged," the letter said.
The palace said that while it would take legal steps, it underscored that people who read the publications that use such photos are unaware of how they are obtained. It said it wanted to encourage debate on child protection issues.
"The Duke and Duchess are determined to keep the issues around a small number of paparazzi photographers distinct and separate from the positive work of most newspapers, magazines, broadcasters, and web publishers around the world," the letter said.