He will be back in Manukau District Court on June 24.
The defendant, dressed in a white T-shirt, cried at times during the hearing and his friends and family shouted their support as he was led away.
Before the hearing, dozens of the defendant's supporters sat outside the courtroom, praying, weeping and singing together.
"Today is a day of tragedy . . . let us take him home," one man said.
Emergency services confirmed they were called to the Favona Rd address just before midday yesterday.
Neighbours reported hearing a loud bang - like gunfire - around that time, followed by hysterical screaming.
"Someone was crying really loudly. It was very sad sobbing," one neighbour said.
Family friend Sione Tatafu described the victim as a "daddy's girl".
"She was a smart little girl who loved to come kick it with the boys," he said.
The incident yesterday happened as the family were moving out of the house, said Mr Tatafu, who grew up in Onehunga with the girl's father.
He said both sides of the girl's large, extended family were devastated.
Police are yet to confirm whether the defendant was related to the toddler and are expected to release the girl's name later today.
Detective Inspector Faa Va'aelua said yesterday that further charges would be considered at the conclusion of the investigation and police were still trying to establish whether or not the death was an accident.
No one who lived at the house held a firearms licence, he said.
Under the Arms Act, a person found to be in unlawful possession of a pistol can face up to three years in prison and a $4000 fine.
