Australian intelligence agencies are attempting to verify the reported deaths of Australians Khaled Sharrouf and Mohamed Elomar in the Islamic State of Iraq and the Levant (ISIL)-held city of Mosul in Iraq, Australian Foreign Minister Julie Bishop has said.
Both men, who moved to the Middle East to fight for ISIL, previously posed in photographs posted on social media holding heads of Syrians.
Their deaths were first reported by the Australian Broadcasting Corporation (ABC) on Monday night.
On Tuesday, Bishop said the reported deaths raised the possibility of Sharrouf's young family being repatriated to Australia.
Australia's Fairfax Media newspapers reported last month that the Australian family of Sharrouf's Muslim-convert wife, Tara Nettleton, was trying to help her bring her three young boys and two teenage daughters from Syria home to Sydney.
Sharrouf's seven-year-old son horrified the world about a year ago when he was photographed holding the severed head of a Syrian soldier by the hair.
John Kerry, the US secretary of state, at the time described it as "one of the most disturbing, stomach-turning, grotesque photographs ever displayed".
Australian PM announces new counterterror measures
Bishop said Sharrouf's death would have to be verified before Australia considers repatriating the family.
"We understand that there are family members in Syria or Iraq and should these reports be verified, then we will try to be in contact with them," Bishop told the ABC.
But the government will not guarantee that the family can return.
"It would depend very much on the circumstances and the advice that we receive from our intelligence agencies at the time," Bishop said.
Sydney-born Sharrouf, who was also a Lebanese national, was a prime target of legislation to be introduced to parliament on Wednesday that would allow "terrorists" who are dual nationals to be stripped of their Australian citizenship.
The law would automatically strip the citizenship of dual nationals convicted of terrorism offences or suspected of serious terrorism-related offences.
The government has also passed new laws that make it a criminal offence to even visit Mosul or ISIL's Syrian stronghold of Raqqa province, where the Sharrouf family was thought to be based.
The government estimates that up to half of about 120 Australians who have travelled to Iraq and Syria to fight for ISIL are dual citizens.