Police said they had no motive for the crime, having had no ransom demand or other communication from the gunman more than 32 hours after he seized Kahurautete (known as Kahu) Durie as her mother pushed her on a riverside walkway near Wellington just before midday on Saturday.
The man, who wielded a shotgun or rifle, drove off with the baby in a car bearing number plates which police said later had been stolen from a vehicle in Auckland, 660km away, several years ago.
The baby girl is the daughter of Judge Eddie Durie and his wife, Donna Hall, a well-known lawyer, who are both among the most influential people in New Zealand's indigenous Maori population.
Judge Durie (62) is chairman of the Waitangi Tribunal which advises the government on compensation for land and other claims made by Maori people.
Planned in advance
Police said the kidnapper was a Caucasian and the fact he was armed indicated the baby's abduction was planned in advance.
They would not discuss a possible motive, but in the absence of a ransom demand, radio and television speculation centred on it being the action of a criminal sentenced by Judge Durie or a disaffected client of Miss Hall's.
The kidnapper snatched the baby as her mother walked near the banks of the Hutt River, just north of the capital, Wellington, with two teenage nieces and a family dog.
A team of 50 police made house-to-house inquiries in the area of the kidnapping throughout Sunday.
Detective-inspector Stuart Wildon told reporters: "We are working with the family to try to establish a possible motive. At this stage we don't have any."
In a statement released by the police, the baby's mother said: "Baby K is an innocent little girl, she can't speak, walk or even crawl. She needs regular feeding and to be kept warm.
"Please, just wrap her up warmly and deliver her to somewhere where there are people and she will be quickly found."
Police said the kidnapper was in his late 30s to early 40s, about 1.78 metres tall, of slim build and either balding or with close-cropped graying hair. - Sapa-DPA