The Federal Government has received credible information that Australia's most infamous terrorist, Khaled Sharrouf, has been killed in an air strike in the Middle East along with two of his young sons, 7.30 has learned.

Sharrouf and his sons, Abdullah, 12 and Zarqawi, 11, are believed to have been killed by a coalition air strike while driving near Islamic State's de facto Syrian capital Raqqa on Friday, August 11, according to government officials speaking on condition of anonymity.

7.30 is also aware one of Sharrouf's brothers has confirmed the death to a small group of Australian extremists via a message which said his brother and nephews were killed by the US-led coalition.

Photos of Sharrouf's corpse and the corpses of his sons have been seen by members of Australia's extremist community, a law enforcement official speaking on condition of anonymity told 7.30.

Border Protection Minister Peter Dutton told a press conference on Wednesday afternoon he could not confirm the deaths.

"It's always very difficult to confirm these reports, given that we're dealing with war zones in Syria and Iraq," he said.

"The point to make is that no Australian would mourn the loss of Khaled Sharrouf. He's a terrorist, he sought to harm Australians and, if he returned to our country, he would be a significant threat to the Australian public.

"Nobody would want to see Australian children die. Nobody would want to see any children die. But the fact is that Sharrouf and his wife took their children into a war zone. If they have been killed, what other outcome would they expect?"

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First time Australian children believed to have been killed

Khaled Sharrouf went to Syria in 2013. ( ABC News )

Sharrouf has long been the poster boy for the small cohort of Australians who travelled to Syria and Iraq to fight with Islamic State, and his death will be welcome news to the Australian Government.

However, the killing of Abdullah and Zarqawi — both are Australian citizens — will leave the Government open to difficult questions about how Australian children were caught up in the strike on Sharrouf.

This is the first-known time that Australian children are believed to have been killed by a Western air strike in the Syrian conflict, and serious questions will be asked about what role Australia played in the operation that led to their deaths.

Sharrouf, 36, from Sydney, fled Australia for Syria on the passport of one of his brothers in 2013.

His wife Tara followed him soon after, taking their five children with her.

Tara died of health complications in 2015, but the pair's children remained in Syria with their father.

Those children are: Zaynab, 15, Hoda, 14, Abdullah; Zarqawi, and Hamzah, six.

Since being in Syria, Zaynab has given birth to a child by Sharrouf's best friend Mohammad Elomar, who was killed in a 2015 air strike.

Sharrouf's three remaining children are now stuck in Raqqa, where local civilians live an increasingly dangerous existence, trapped between a US-backed offensive and the Islamic State, who are preventing anyone from leaving the besieged city.

Sharrouf was the first Australian to have his citizenship stripped earlier this year under new counter-terrorism legislation. He remained a citizen of Lebanon.

'Australian law get stuffed'

Khaled Sharrouf in an undated photograph. ( ABC News )

Sharrouf first came to public attention in 2005, when he was charged over the Operation Pendennis terrorist conspiracy.

Pendennis involved groups of men in Sydney and Melbourne gathering guns, ammunition and bomb-making equipment to use in terrorist attacks in both cities.

During his trial it was stated that Sharrouf had been diagnosed as a paranoid schizophrenic.

The court also heard of remarks he made about Australia, that were secretly recorded by police.

"Forget Australian law … Australian law get stuffed, finished … give us all back our passports and we leave," he said.

"I swear to God I'll be the first to get out of this stuffed-up country. Sons of dogs.

"I swear I'd rather be locked up and tortured and everything in a Muslim country rather than be locked up one day in this country."

He was a peripheral player and only served five years in jail.

In the years after his release it became clear he had not abandoned his commitment to militant Islam, and in 2012 was a participant in the Hyde Park riot that began as a protest against a YouTube video denigrating Islam's prophet, Mohammed.

Sharrouf moved to Syria the next year to join the war being waged by Islamic State against dictator Bashar al-Assaad.

In 2014, Sharrouf attained global notoriety when he published social media photographs of Abdullah, then aged nine, holding the severed head of a Syrian government soldier in Raqqa.

Even US secretary of state at the time, John Kerry, reacted to the photo.

"This image is really one of the most disturbing, stomach-turning, grotesque photographs ever displayed," he said.

Sharrouf returned to the public consciousness in May this year when a video emerged of his youngest son Humzah being coaxed by his off-screen father to simulate the killing of non-Muslims and Australians.

A week later police raided the home of one of Sharrouf's relatives following concerns the pair may have spoken about committing a terrorist act on Anzac Day.