A New Zealand court on Wednesday found a woman guilty of murdering her three young daughters after a harrowing month-long trial.

Lauren Dickason was accused of strangling and suffocating her twins Maya and Karla, aged two, and first daughter Liane, six, while her husband was out to dinner with colleagues, according to local media reports.

Dickason admitted killing the girls, but had argued a defence of insanity and infanticide.

Under New Zealand law, infanticide is a defence for a mother who causes the death of her child when, "at the time of the offence, the balance of her mind was disturbed".

The girls were killed at their home in the South Island city of Timaru soon after the family arrived in New Zealand from South Africa.

A jury at Christchurch High Court found Dickason guilty of all three charges of murder. 

As the verdict was handed down, Dickason's lawyer looked on in shock.

In New Zealand, murder carries a prison sentence of at least 10 years.

Following the verdict, Detective Inspector Scott Anderson said in a statement that police extended their "sympathies to the families who will never get to see Liane, Maya, and Karla grow up".

"Words cannot begin to express the tragic circumstances of this investigation," he added.

During an emotional trial, the prosecution and defence lawyers had agreed Dickason was mentally unwell when she killed her children.

However, they differed as to whether her mental state was such that she was not fully aware of what she was doing.

In court, crown prosecutor Andrew McRae told the jury that anger had driven Dickason to murder her children.

But Dickason's lawyer Kerryn Beaton had argued that the girls deaths were not due to anger and resentment, but were the result of a "severe mental illness".