The shocking discovery was made after the luggage was sold at an auction for abandoned goods in a storage unit in South Auckland.
Police have launched a homicide investigation.
Early indications are that the children could have been deadfor a number of years before being found, the New Zealand Herald reports.
Police are still in the early stages of the investigation, Detective Inspector Tofilau Faamanuia Vaaelua explained, but the children appear to have been dead for a number of years.
He said the children were aged between five and 10 and police were working on establishing when and where they died.
“What I can say is we are making very good progress with DNA inquiries,” he told the New Zealand Herald.
Relatives of the victims “were in New Zealand”, he said, but police were also working with Interpol.
The family who bought the suitcase, from Clendon Park, are said to have unwittingly bought the bag on August 11 from a local storage facility as part of a trailer-load of “unowned” goods.
The human remains were found inside the case as it was unpacked at their home.
One neighbour told New Zealand media outlet Stuff they had noticed a “wicked smell” in the vicinity of the house on Thursday.
The man, who works in a crematorium, said he recognised it as being the smell of human remains.
“I knew straight away and I thought where is that coming from,” he told Stuff.