Islamic State terrorist Khaled Sharrouf and his two sons have reportedly been killed in Syria.
Attorney-General George Brandis said he was aware of the media reports, but the government's capacity to confirm reports of deaths in Syria or Iraq was "extremely limited" because it was a war zone.
"But, if the reports are true, Australia will not mourn Khaled Sharrouf. He committed some of the most horrific crimes and waged war on Australians and our way of life," Senator Brandis said in a statement on Wednesday.
Media reports cited unnamed government officials as confirming Sharrouf - who fled Australia in 2013 to join extremist forces - and his sons Abdullah, 12, and Zarqawi, 11, were killed in a coalition air strike while driving near Raqqa on August 11.
Immigration Minister Peter Dutton said nobody would want to see Australian children die, but their parents had dragged them into a war zone and should have expected nothing less.
"They are obviously horrible people - atrocious parents - to take their children into that war zone," he told reporters in Canberra.
"You've seen the footage of the children - one holding up a severed head and the rest of it - who would expect any other outcome from parents and people as evil as their father."
Photos of Sharrouf's corpse and the corpses of his sons had been seen by members of Australia's extremist community, the ABC reported.
If confirmed it would be the first known deaths of Australian children by a coalition air strike in the Syrian war.
In February, Sharrouf became the first Australian to be stripped of citizenship under new anti-terrorism laws.
"Khaled Sharrouf and his wife took their children to an active war zone, and exposed them to the barbaric practices of Islamic State," Senator Brandis said.
The IS fighter made headlines in 2014 when he posted a photograph of one of his sons holding the head of a Syrian government official.
Sharrouf went to Syria on his brother's passport just a year after completing a four-year jail term for plotting a high-level terrorist attack in Australia.
He was caught during a major counter-terrorism investigation that broke up jihadist cells in Melbourne and Sydney.