But on Friday, Bauer chief executive Paul Dykzeul told the Herald on Sunday: "The photos we published were taken in a public place and are therefore legal."
When asked if the company would heed the Carters' request and not publish unauthorised photos of their children in the future, he replied: "That would depend entirely on the circumstances at the time."
He confirmed the controversy had led to a review by Bauer top brass into content, including whether it would continue to publish unauthorised photos of the children of New Zealand celebrities.
"We have concluded that our processes are sound and we will continue to assess each potential publication as it arises," Dykzeul said.
Dykzeul said the publishing company responded in writing to the Carters' lawyers on Wednesday. But he would not elaborate.
Neither Carter's legal team nor his management would comment this week.
Psychologist and parenting advisor Nigel Latta and broadcaster Mike Hosking were among those critical of the publishing of the pictures.
