The baby abducted at gunpoint in Lower Hutt yesterday is the daughter of High Court judge Eddie Durie and Wellington lawyer Donna Hall.
Eight-month-old Kahurautete Durie was abducted as she was being wheeled by Ms Hall in a pushchair shortly before midday.
Ms Hall was walking with Kahurautete's young cousins andtheir dog along the tree-lined St Albans Grove.
The kidnapping appears to have been well planned, police said.
Justice Durie is the chairman of the Waitangi Tribunal and presided over the trial of Rachealle Namana, the woman who pleaded guilty to the manslaughter of Wairarapa 2-year-old Hinewaoriki Karaitiana-Matiaha - known as Lillybing.
Police are seeking a man described as Caucasian, aged in his late 30s or early 40s, about 1.79m tall with balding or close cropped hair.
He was wearing black jeans and black jacket.
At the time Kahurautete was abducted she was wearing a navy blue, one-piece, "stretch and grow" with a dark pink skivvy underneath. She also had a light pink hooded jacket with a distinctive hood with rabbits ears attached to it.
Police said there was no indication the kidnapper was known to the family, Radio New Zealand reported.
Police are also seeking a late model two-toned silver and blue Mitsubishi car, registration UL3802 or similar.
Ms Hall urged anyone with information on the abduction to contact police on 0800 150 499.
"Baby K is an innocent little girl, she can't speak, walk or even crawl. She needs regular feeding and to be kept warm," she said in a police statement.
"Please, just wrap her up warmly and deliver her to somewhere where there are people and she will be quickly found."
