Wayne Godinet, 34, and his young boys perished when the blaze tore through the property on Russell Island near Brisbane about 6am on Sunday.
The children's mother, Samantha Stephenson, 28, and another woman survived the inferno, fleeing as the two-storey home was engulfed in flames.
The blaze damaged two neighbouring homes and left several people needing treatment for minor burns and smoke inhalation.
In an update on Friday, police said extensive investigations had failed to identify the cause of the fire.
"Despite this, no suspicious circumstances have been identified," police said.
Detective Superintendent Andrew Massingham said on Monday police were keeping an "open mind" into whether the fire was suspicious because some elements required closer scrutiny.
Autopsies have been completed and "an extensive report" will be prepared for the coroner.
The victims' families have been updated on investigations and they continue to receive support.
Police thanked the community for its ongoing support since the tragedy and continued to appeal for information that might help the investigation.
The deadly blaze left the small Moreton Bay community in shock and looking for answers as they pay tribute to the children aged 11, 10, twin four-year-olds and a three-year-old.
A number of Mr Godinet's relatives travelled from around and Australia and New Zealand to Russell Island to pay their respects.
They gathered on Thursday to perform a traditional Maori ceremony near the home's charred remains.
Nearly $35,000 has been raised via a Go Fund Me page for Ms Stephenson, while other funds continue to raise money for affected families.
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