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A 48-year-old man, believed to be the father and husband of the four found dead at the Tullamarine home, was expected to be formally interviewed by homicide detectives on Thursday night.
He provided an initial version of events after police arrived at the Burgess Street property and discovered the bodies of a 42-year-old woman, two girls - aged seven and five - and a three-year-old boy.
It is understood the uninjured man made the call to emergency services.
Acting Deputy Commissioner Robert Hill acknowledged the man was a person of interest, but warned against people jumping to conclusions.
"We have a long way to go before we can actually understand and appreciate what occurred," he said.
There is no history of violence associated with the family and a potential murder-suicide situation is being considered as part of the investigation.
"There are a number of possibilities," Mr Hill said.
"And that's one that could possibly be relevant to this event."
Mr Hill refused to divulge the nature of the injuries suffered by the mother and her children.
"The loss of life is tragic in any circumstances," he said.
"But when it involves children, it makes it even more heart-wrenching."
Police, homicide detectives and forensic investigators were expected to remain on-site throughout Thursday evening, methodically piecing together the circumstances of the tragedy.
No one else is being sought over the deaths and there is no risk to the community.