SYDNEY (AFP) - An Australian man has been killed in Syria fighting Islamic State in Iraq and Syria (ISIS) militants, the country's third national thought to have died alongside Kurdish forces, reports said on Monday (May 30).

Former Australian soldier Jamie Bright, in his 40s, was named on social media as having been "martyred" in recent days. The Kurdish People's Protection Unit said on its Facebook page that Mr Bright died alongside three other Kurdish fighters.

"He was shot about three or four days ago," an Australian friend who fought alongside Bright in Syria told News Corporation Australia.

The friend, who was not named, said Mr Bright had travelled to Syria in early 2015 because he "saw something was happening that wasn't right and wanted to fix it".

"He saw governments doing nothing. He saw it as wrong and believed it had to be changed," he added.

Australia's Foreign Ministry said it could not verify if Mr Bright had been killed as the "government's capacity to confirm reports of deaths in Syria is extremely limited".

"If confirmed, this latest death is yet another tragic reminder of the dangers involved for those who seek to travel and fight in conflict zones," it added in a statement.

At least two other Australians, Reece Harding and Ashley Johnston, were killed in 2015 while with Kurdish groups fighting ISIS.

Prime Minister Malcolm Turnbull said "Australians must understand that if they go and fight in conflicts like that, they are breaking Australian law".

"If they come back within Australia's jurisdiction, they will be held to account for that."

Under new laws designed to stop citizens travelling overseas to join militant groups, it is a crime to fight for militants on either side of the conflict in Syria.