Australians Khaled Sharrouf and Mohamed Elomar, who have shocked the nation and the world with their bloody exploits with the Islamic State terror group, have reportedly been killed in Iraq.

The federal government said on Monday night it was working to confirm the deaths, which the ABC said were believed to have happened in the Islamic State stronghold of Mosul in the country's north.

While there is little ground fighting in Mosul, coalition air strikes are being carried out in the area. This raises the possibility that the two men were targetted by coalition bombing raids based on precise intelligence, or were killed incidentally in raids aimed at other targets.

The friends from Sydney have gained notoriety with their violent rampage across strife-torn Syria and Iraq, the macabre details of which have been splashed across social media.