The woman, 42, appeared in court on Wednesday after she was returned from South Korea.

The bodies of her children were discovered by a family in Auckland, who bought the suitcases in August in an online auction of items abandoned in a storage unit.

The judge at Manukau District Court imposed a temporary order that keeps many details of the case secret, including the names of the woman and the victims.

She was not required to enter a plea at the hearing.

The children were aged between five and 10 when they died, detectives have said, and their bodies had been in storage for at least three or four years.

Officers have emphasised that the family who found the bodies had nothing to do with the deaths.

South Korean police say the mother was born in South Korea and later moved to New Zealand, where she gained citizenship.

Immigration records show she returned to South Korea in 2018.

"With the extradition, we hope that the truth of the case, which has garnered worldwide attention, will be revealed," the South Korean justice ministry said.