The man, who is the biological father to one of the girls, told 7 News the community had a right to know how two-year-old Darcey-Helen and 1-year-old Chloe-Ann died.
“I want a full public inquiry into the deaths of my girls,” he said.
“I want those responsible for the inaction that led to my kids being exposed to the situation that they were in to be held accountable.
“I want to expose the truth. The community has a right to know.”
Darcey-Helen and Chloe-Ann died inside a black station wagon parked across the front yard of their family home in Logan, south of Brisbane, on Saturday.
Their mother, 27-year-old Kerri-Ann Conley, has now been charged with their murders, as well as possession of dangerous drugs and possession of drug utensils.
She is the first person to be charged under the Queensland’s expanded definition of murder, which includes reckless indifference to human life.
Queensland Premier Annastacia Palaszczuk said the family was known to the state’s child safety department which had contact with them in the past.
She said Attorney-General Yvette D’Ath would ask Cheryl Vardon, the Queensland Family and Child Commission’s principal commissioner, to investigate, and those findings will then be released.
“The death of these two young girls is an absolute tragedy,” she said on Monday.
“I was heartbroken when I heard about it. I think everybody would be in exactly the same position.”
A woman who babysat the two girls told news.com.au that authorities had been alerted about the family before.
Gina McKenzie, who said she was the last person to see the girls about 8.30pm on Friday, claimed there had been previous complaints to authorities about the children’s welfare.
“I know welfare had been called numerous times,” she said.
“I strongly believe they should have done much more.”
Family and friends of Ms Conley claim they also made multiple attempts to alert the authorities to their concerns for the children.
Conley did not appear when her matter was mentioned at Brisbane Magistrates Court on Monday.
She was remanded to appear in Beenleigh Magistrates Court on December 11.
A man was assisting police with their inquiries but was no longer being questioned.
Paramedics were called to the home in the Waterford West suburb of Logan on Saturday afternoon but could not revive the sisters.
The girls were declared dead at the scene and police say they showed signs of being exposed to extreme heat.
Child Safety Minister Di Farmer has said her department will offer police any assistance needed in their investigation.
Deb Frecklington, leader of the Liberal National Party opposition, wants to know how the department was involved with the family, and said the government would have her full support in overhauling the child safety system.