The Australian man who killed himself and several others in a suicide bomb attack in Iraq last week was an 18-year-old from Melbourne.

The Federal Government believes he was 17 at the time he left Australia.

The attack happened in the centre of the Iraqi capital Baghdad on Thursday, near the Shiite mosque of Abdullah bin Rawah in the main wholesale market of Shorja.

The Islamic State named the man as Abu Bakr al-Australi on an affiliated Twitter feed.

Attorney-General George Brandis says the man is the second Australian suicide bomber in the Iraq and Syria conflicts.

"This is a disturbing development and is a further example of the dangerous and volatile situation in Iraq at present," he said in a statement.

"The Government deplores the violent actions being undertaken by ISIL and other extremist groups in Iraq and Syria, and is deeply concerned about the involvement of Australians in these activities."

The Islamic State - previously known as the Islamic State of Iraq and Syria (ISIS), or the Islamic State of Iraq and the Levant (ISIL) - has been outlawed in Australia and listed as a terrorist organisation.

"As I have said many times, it is illegal for Australians to engage in the conflicts in Iraq and Syria and the Government urges Australians not to travel to the region," Senator Brandis said.

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"The participation by Australians in the conflict in Iraq and Syria poses a significant domestic security threat to Australia when those involved return home and seek to pursue violence here.

"The Government will continue to take all necessary measures to keep Australia and Australian interests safe."

Foreign Minister Julie Bishop last week said the Government was working hard to prevent Australians being radicalised.

"We're doing all we can to prevent people going overseas as foreign fighters," she said.

Earlier in July several senior Islamic leaders met with the Attorney-General in Canberra to discuss the problem of so-called home-grown terrorism.

They vowed to do what they can to stop young Australians heading overseas to fight alongside extremists.