Pediatrician Tareq Kamleh, colloquially known as "Doctor Jihad", travelled to Syria in 2015 to join the terror organisation.
He was assumed to have been killed in 2017's final siege of Raqqa, the de facto capital of the self-proclaimed Islamic caliphate in Syria.
But it has since been revealed Kamleh is one-of-13 men linked to the terror group who are imprisoned in Iraq and want to return to Australia.
The Australian newspaper reported on Wednesday he didn't die in the siege as his family believed.
Labor frontbencher Clare O'Neil said she didn't want Kamleh to ever return to Australia and he should "rot in jail".
"He's obviously made a decision to join a violent death cult and he needs to be accountable for that," she said.
But fellow senior minister Murray Watt said the government faced constitutional limitations on preventing Kamleh, an Australian citizen, from returning.
"Anyone who returns to Australia who's been part of these sorts of organisations will face the full force of the law," Senator Watt told Nine's Today program.
"We won't be providing assistance, just as we haven't provided assistance to others to come back."
Opposition Leader Angus Taylor said the government needed to do more to prevent Islamic State-linked Australians from coming back.
"We have put legislation in front of the parliament to prevent third parties from helping people like him - terrorists - back into the country," he said.
Senator Watt said the opposition was acutely aware of constitutional limitations and should not be pushing the government to do things beyond its ability.
At least 16 Australian women who left the country to marry jihadists have returned since 2022.
Several have since been charged with offences linked to their time overseas under the Islamic State umbrella.
Kamleh is wanted by the Australian Federal Police under an active warrant for terrorism offences, which include joining and recruiting for a banned organisation.
He studied medicine at the University of Adelaide before further training at Royal Adelaide Hospital and the Women's and Children's Hospital.
His registration was suspended in 2015 after he appeared in an Islamic State video that featured a premature baby.
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