In a statement today, Vaaelua confirmed the identification process has been completed.
However, he said the Coroner had issued an interim non-publication order which suppressed the 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.
"Police are continuing to investigate the circumstances surrounding the death of the children."
A woman who is believed to be the children's mother is in South Korea and could face extradition to New Zealand.
The family member is being sought by South Korean police in connection with the discovery of two children's remains earlier this month.
A police officer told Reuters the woman was a Korean-born New Zealander who arrived in South Korea in 2018. There was no record of her departing South Korea since then.
Her whereabouts are unknown and it is unclear whether she had other relatives with her when she arrived in South Korea, Reuters reported.
"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.