Police have identified the two children whose bodies were found in suitcases from an abandoned storage unit in Manurewa.
In a statement, Detective Inspector Tofilau Faamanuia Vaaelua said the identification process had been completed.
Both children had now been identified, he said.
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.
The order suppresses the names of the children and their relatives, as well as evidence that may lead to the identification of the victims.
Vaaelua said police were continuing to investigate the circumstances surrounding the death of the children.
The bodies were discovered earlier this month, after a Clendon Park family won an auction for abandoned goods in a storage unit, without realising what was inside.
After bringing the goods home, they discovered human remains inside two suitcases, which were later identified as two primary school aged children.
The Associated Press has reported that a relative of two children was likely in South Korea.
An official at Korea's National Police Agency told the Associated Press the woman was a Korean-born New Zealander in her 40s who arrived in South Korea in 2018.
Vaaelua has said that police were working with international criminal police agency Interpol in their homicide investigation.