Detective Inspector Faa Va'aelua told media at a press conference today that a firearm had been found at the address.
Mangere MP Su'a William Sio says he understands authorities are treating the shooting death of a 2-year-old girl as a horrible accident.
"When I spoke to police they were still going through forensic evidence and conducting interviews to get a better idea of things but I understand they were leaning towards declaring it as a tragic, horrible accident."
Mr Sio called on the community to allow the family to grieve.
"The parents appeared to be a loving couple. Not a lot of us knew the family, all we know is that the child died under tragic circumstances.
"No amount of punishment, or ridicule, or judgement by the general public is going to take away from the pain and grief the family feels."
In a Facebook post, the MP said police were still analysing forensic evidence they'd gathered and finalising interviews to get a clearer picture of what occurred.
"I understand that the father of the dead child is wracked with grief, pain and anguish from the death of their child, and when the police come to the conclusion of their investigation, and whatever that conclusion maybe, this father (parents) will have to live with the tragic death of their child for the rest of their lives."
Police cordons remain in place at the Mangere house where a toddler was shot dead.
An officer and one police car are at the front of the property, where a child's pink tricycle can be seen through the fence. A large green tarpaulin is also covering part of the fence and officers in white boiler suits are examining the site.
A woman in a neighbouring house told the Herald this morning she used to see the 2-year-old girl playing on the bike in the family's garden with a man she thought was the girl's father.
"She would pedal this way to the house and the father would turn the little bike around for her.
"I thought: 'Oh, what a good man'."
Police and St John were called to the Favona Rd property just before midday yesterday.
A child was pronounced dead at the scene and police officers quickly swarmed the area; blocking off a large part of the busy main road as they worked at the scene.
Neighbours reported hearing a "loud explosion" -- thought to be gunfire -- shortly before the sounds of hysterical sobbing.
People at the scene on Favona Rd in Mangere. Photo / Jason Oxenham
A 26-year-old man is due to appear in the Manukau District Court this afternoon, charged with unlawful possession of a pistol.
He was due to appear this morning, but the hearing has been postponed to give him a chance to speak further with lawyers.
Police said further charges will be considered after an investigation and officers were working to establish whether or not the death was accidental.
Authorities confirmed no one who lived at the house held a firearms licence and that the girl was shot dead with a sawn-off shotgun -- classified as a pistol under the Arms Act.
Speaking about yesterday, the neighbour said she heard crying coming from over the fence and saw a woman in the garden making a phone call.
It wasn't until police knocked on her door a few hours later that she discovered what had happened.
Tributes to the toddler and her family have begun appearing on social media websites this morning; as friends and family members come to grips with what happened.
One relative said: "Can't believe [you're] gone, baby girl."
Another family member said she was "heartbroken and shocked" at the events and had been crying all night.
Police at the scene of the shooting. Photo / Tess Nichol
Photos posted by family members show a chubby-cheeked toddler with a big smile.
The toddler killed was one of four children who lived at the Favona Rd property. The family had moved to the area from nearby Onehunga about six months ago, the neighbour said.
The neighbour, who had lived in the same house for 25 years, said this sort of thing had never happened before.
"It's a very quiet area. It's really out of the blue."
