Officers were called to the home about 12.20pm yesterday, where they discovered the bodies of Katie Perinovic, 42, her three-year-old son Matthew and two daughters Claire and Anna, aged seven and five.
The husband and father, Tomislav Perinovic, 48, called emergency services to report the deaths.
Acting Deputy Commissioner Bob Hill said the man was "assisting police with their enquiries", but stressed the investigation was ongoing and it was "very important we do not speculate".
But he said the father had provided an account to police, and investigators did not believe any other parties were involved.
"He is a person of interest and he is assisting police with our enquiries," Acting Deputy Commissioner Hill said.
"But we should not draw any conclusions at this point in time as to his culpability. If one was to do so, that would be grossly unfair."
He said as far as police were aware, there was no history of family violence in the household.
Acting Assistant Commissioner Mark Galliott said the sudden loss of life, including three children, was "difficult to comprehend".
"This will have long-lasting effects on the police that attended, on extended family, the community, the neighbourhood, the emergency services and everybody else involved," he said.
"They'll be lifelong memories that they'll have to deal with and so we'll make sure that the welfare of our members and the emergency services that attended are paramount."
Neighbour Marie Groves told the ABC her children had shared playdates with the family, who attended her daughter's birthday party late last year.
She said she was devastated by the news, describing Katie Perinovic as "the best mum".
"It's so close to home, these are people who've spent time in my home, my kids love their kids," Groves said.
"How am I going to tell my kids?"
She said Ms Perinovic was a physiotherapist who had only recently returned to work after taking time off to care for her young son Matthew.
Another neighbour, John Constantino, said everyone on the street was in shock.
He said Ms Perinovic was "one of the nicest people you'd meet", and recalled how she was often out and about with her children, who were always friendly and polite.
"She was well liked around here."
Another neighbour, Tara, said the "gorgeous, very friendly and happy" children sometimes played together in the park.