Authorities identified on Monday the three people who were found dead in the remains of a suspicious Bonner house fire as Anne Muhoro, 45, her son Ezvin, 8, and her daughter Furaha, 5.
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ACT Policing's Detective Superintendent Scott Moller would not comment on the cause of death on Monday, saying the results of the autopsies had not yet been released.
But he acknowledged the impact the deaths had had those who knew the family.
"This is a tragic situation and everyone gets affected by it," he said. "And everyone that we've spoken to is heartbroken."
The family are Australian citizens and have next of kin both in Australia and overseas.
Superintendent Moller would not be drawn on whether the focus of the investigation was on a murder-suicide, or a murder suspect.
"This is very early days in this investigation and I'm not going to, at this time, speculate on how it's going to be finalised," he said.
"[There are] multitudes of avenues of inquiry that we have, we'll be following every one of those."
He called on Monday for members of the public to come forward with any dash cam footage taken in Bonner between 12am and 8.45am the morning of February 19.
In response to a question about the man police earlier took into custody, Superintendent Moller said many people were helping police with their inquiries.
He said the family's bodies had been identified by a complex process of DNA matching.
He said all the evidence had been collected from the scene of the fire but forensic testing was ongoing.
He urged anyone with information to call Crimestoppers on 1800 333 000.
Fire crews arrived to find a house "well alight" on Peter Coppin Street just before 9am Monday, February 19.
At first, crews found no one inside during a preliminary search of the house but made the grim discovery after putting the fire out.
Detective Superintendent Moller has previously said it was too early in the investigation to speculate on the circumstances surrounding the deaths, but fire accelerants had likely been used across multiple "seats of fire" in the house.
On Tuesday, ACT minister Yvette Berry offered her condolences to the family and acknowledged the work of both police and firefighters.
"There are many people in our community that have been affected by this tragic event," Ms Berry said.
"While we process this loss as a community, it is important that we remember this is an ongoing police investigation and a report is being prepared for the ACT Coroner. We need to respect the privacy of the individuals involved."
In the days after the blaze, flowers and soft toys were left near the property in tribute as Canberra police worked at the scene.
Several neighbours expressed their shock at the tragic news and said the family who lived there had mostly kept to themselves.
Anyone needing support could contact Lifeline on 13 11 14, Ms Berry said.
