An Australian politician is under investigation after allegedly travelling to Syria to join Kurdish forces in the fight against Islamist extremists.

Matthew Gardiner, 43, the head of the Labor Party in the Northern Territory and a former soldier, is believed to have made contact with Kurdish fighters through social media and travelled to join them in the war-torn country.

The Government has said Gardiner, who served as an engineer in Somalia in the 90s, faces jail despite the Kurds and Australian military both fighting Isis (Islamic State).

Peter Dutton, the federal Immigration Minister, said he did not want to see Australians killed "regardless of whether they are well-intentioned".

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"We don't want to see cowboys running off whether or not they have been trained or whether they were part of the Australian defence force," he told Sky News.

Labor, in opposition in the Northern Territory, said it had sacked Gardiner as president of the territory's branch.