The children, twins aged three and the other, seven, had moved to the South Island suburb of Timaru in the last week after getting out of quarantine.
A woman was transported to Timaru Hospital in a stable condition.
Neighbours Karen and Brad Cowper called police when they heard a man screaming and crying, the Stuff news organisation said
They said they asked the man if he was OK but he didn’t respond other than to say: “Is this really happening?”
A police officer stands in the driveway of a house where three children were found dead
/ AP“We went outside and realised it was coming from the neighbouring property.
“Everything got cordoned off. We weren’t sure what had happened but we knew something significant had happened.”
She said she saw a woman being supported while she walked into an ambulance and a man being taken away in a police car.
Timaru Mayor Nigel Bowen said the community will be devastated by the tragedy after five teenagers were also killed in a horrific car crash on August 7.
“Again, unfortunately. It seems that the community has had layers of tragedy with the five young lads that passed away so it’s really tough,” he said.
He said the area where the incident took place is “just a typical suburb” and relatively quiet.
“I think the community will be thinking, why is it happening to a place like ours?
“There’s a lot of pressures on society at the moment, you have to question the support around mental health, are we doing things right in this country? I question that we’re probably not.”
