Hakyung Lee is charged with killing Minu Jo, 6, and Yuna Jo, 8, in June 2018. She was extradited from South Korea to face the charges, which she denies.
The children's remains were found inside luggage at an abandoned storage unit in Auckland in August 2022.
Lee, who is a New Zealand citizen, had travelled to South Korea and changed her name in 2018, shortly after the children are believed to have been killed.
She was born in South Korea and went by the name Ji Eun Lee previously.
A jury was chosen on Monday for Lee's trial at the High Court in Auckland, and the matter is expected to take four weeks.
Prosecutors are due to outline their case on Tuesday and said they would call 40 witnesses.
New Zealand news outlets reported Lee was representing herself, although two lawyers were on standby to help her if needed.
She did not speak during the hearing on Monday and shook her head, rather than answering through an interpreter, when asked how she pleaded to the charges.
Not guilty pleas were entered by Justice Geoffrey Venning, who is presiding.
The children's cause of death remains unknown. Court documents said they might have been killed by sleeping medication prescribed to Lee and detected in their bodies by forensic investigators, but another cause of death hasn't been ruled out, according to Radio New Zealand.
Lee's husband died in 2017 after a period of deteriorating health, according to RNZ. Justice Venning told the jury on Monday they would likely be asked to consider the matter of Lee's sanity at the time of the alleged killings, news outlet Stuff reported.
Venning said the trial would be distressing to Lee and has granted her permission to watch proceedings from another room in the courthouse, Stuff said.
The children's remains were discovered after Lee stopped paying rental fees for the Auckland storage unit when she ran into financial difficulties in 2022, RNZ reported. The locker's contents were auctioned online and the buyers found the bodies inside.
Lee, who is in her 40s, was arrested in September 2022 in South Korea and extradited two months later. She had granted consent in writing to be extradited after a formal request from New Zealand to return her to face trial, South Korean officials said at the time.
South Korea's Justice Ministry said it had provided New Zealand with unspecified "important evidence" in the case.
Lifeline 13 11 14
beyondblue 1300 22 4636
10°C