Australia is close to confirming the reported death in Iraq of two home-grown militants who shot to infamy last year after being photographed holding the severed heads of Syrian soldiers, Foreign Minister Julie Bishop said on Tuesday.

Australia issued arrest warrants for suspected Australian Islamic State fighters Khaled Sharrouf and Mohamed Elomar after the images, which also showed Sharrouf's 7-year-old son holding one of the heads, caused a global outcry.

The pair are believed to have been killed in an airstrike on the Iraqi city of Mosul, which is under the control of the Sunni militant group. Their deaths were first reported late Monday by the Australian Broadcasting Corporation.