Police say they've identified the children found in suitcases in Manurewa.
Two young children, believed to be between five and 10, were found amongst the abandoned contents of a storage unit earlier this month after they were bought at an auction.
Police are treating the case as a homicide and say the bodies may have been there for several years.
"Police investigating the deaths of two children, located on August 11 in Manurewa, are now able to confirm the identification process has been completed," Counties Manukau District Crime Manager Detective Inspector Tofilau Faamanuia Vaaelua said in a statement on Friday.
"However, the Coroner has issued an interim non-publication order which suppresses evidence of the identities of the children at the request of their family.
"This order suppresses the names of the children and their relatives, and evidence that may lead to the identification of the two victims."
South Korea police say a woman believed to be a family member of the two children arrived in their country in 2018.
"New Zealand police had requested confirmation whether the person who might be related to a crime case was in South Korea," the police officer said, adding that given her past address and age, she could be the mother of the children.
Det Inspt Vaaelua said police are continuing to investigate the circumstances surrounding the death of the children.
"Further updates will be provided as the police investigation allows."