Some paparazzi had gone to “extreme lengths” to take pictures and “a line has been crossed”, the palace said.
It wants to “inform discussion” on unauthorized photography of children.
The Kensington Palace said a small number of media organizations, mostly in Germany, France, Australia, New Zealand and the US, had published photos of two-year-old Prince George in “unacceptable circumstances”.
However, it said the “vast majority”, and all UK publications, had refused.
The palace says in recent months, photographers have:
The palace said the most recent incident, which was last week, involved a photographer who was discovered by police lying down in the boot of a rented car attempting to shoot photos outside a children’s play area.
Kensington Palace tweeted: “The Duke and Duchess want to extend their thanks for the kind and supportive messages they have received in recent months.
“They have been delighted to share photos of their children and will continue to do so in the months and years ahead.
“Yet undercover paparazzi continue to pursue their children, selling images of Prince George to international publications.”
In the published letter, Kensington Palace communications secretary Jason Knauf said Prince George had become the paparazzi’s “number one target”.
He said: “It is of course upsetting that such tactics – reminiscent as they are of past surveillance by groups intent on doing more than capturing images – are being deployed to profit from the image of a two-year-old boy.
“In a heightened security environment such tactics are a risk to all involved.
“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.”
Jason Knauf said Prince William and Kate Middleton wanted Prince George and his sister Princess Charlotte “to be free to play in public and semi-public spaces with other children without being photographed”.
They want to give their children a childhood that is “free from harassment and surveillance”, he said.
The Metropolitan Police said in a statement: “The covert actions of photographers have at times caused concerns during police protection operations when they have been considered a possible security threat.
“Photographers are potentially putting themselves at risk from armed intervention where our armed officers perceive a risk to the personal safety of their principal, the public and themselves.”
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