Western Australia assistant police commissioner Paul Steel said: "This is early and we've not yet fully examined the scene".
Cops went to the property in the northern suburb of Perth after a man visited a regional police station and told them about the scene.
A man, said to be in his 20s, is in custody and being questioned after presenting himself to police.
Police confirmed they did not know how long the bodies had been inside the Bedford house.
Forensic police and the homicide squad are undertaking a "meticulous" investigation of the Bedford crime scene which "could take a number of days".
A neighbour told Ten Eyewitness News the property is home to a couple and their three young children.
The police chaplain was at the scene providing support for police officers on Sunday.
Investigations are ongoing and while a man remains in police custody over the incident, no charge have been laid.
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"It's just really sad that something like this can happen in such a quiet neighbourhood, it's horrid on every level. poor children", resident Maria Manfredini said.
Mr Fairbrother said he understood the family may have been killed "sometime in the last week" but they had been overseas at the time.
"This is a tragic event and it will no doubt have an impact on not only on the family and friends of the deceased, but on the whole of the community, those first responders who are faced with attending a scene with deceased people".
Violent crime with multiple victims is rare in Australia but this was the second major incident in Western Australia this year.
The bodies of Peter Miles, 61, his 58-year-old wife Cynda, their daughter Katrina, 35, and her four autistic children with estranged partner Aaron Cockman - Taye, 13, Rylan, 12, Arye, 10, and Kadyn Cockman, 8 - were found at the Miles residence.
He also could not confirm the ages, genders and relationship of the deceased.
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