Life is the maximum sentence for the crime.
In June last year Tania Shailer and David Haerewa were jailed for 17 years for the manslaughter of three years-old Moko Rangitoheriri.
Gustav Otto Sanft, who is of Tongan descent, appeared in the High Court yesterday following the death of his two years-old daughter in a shooting incident.
Kaniva News reports Sanft appeared before Mr Justice Geoffrey Venning.
The trial is expected to last three weeks.
Sanft, 26, has pleaded guilty to unlawful possession of a pistol, as the sawn-off shotgun was technically classified.
It was reported last year that he also faced charges of possessing cannabis for supply.
The High Court was told that Amokoura Daniels-Sanft died after she was shot in the head at close range with a sawn-off shotgun on June 2, 2016.
She was in the drive way of the family home at the time of the incident.
The court was told Sanft aimed the gun at his daughter’s head because he was frustrated that she was jumping on some couches.
The family was moving house at the time.
The house in Favona Rd, Mangere, was occupied by Gustva Otto Sanft, Amokoura Daniels-Sanft, her three siblings and their mother Julia Daniels.
The Crown alleges that Sanft was responsible for his daughter’s death, but did not mean to harm her.
Sanft’s defence argued the gun had fired accidentally.
The day before the incident Sanft’s older children found a weapon wrapped in a sheet in a cupboard.
The court was told the shotgun’s barrel and stock had been sawn off and the serial number ground off.
Police said nobody at the house had a firearms license.
The name of the accused and the daughter were originally suppressed.