Members of non-English speaking communities have reportedly been among more than 100 Australians believed to have travelled to Syria to fight in the conflict, born of an anti-government uprising in early 2011.
Senator Carr says he cannot comment on Australian Federal Police investigations into Australians who may have engaged in combat in Syria, and warns that doing so breaks Australian law.
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But he says he's confident members of migrant communities understand they shouldn't participate in the Syrian conflict.
"We're in Australia. Common sense prevails. People understand that this is not a dispute for Australians to take up arms about. What we say - and this is our multiculturalism that we value so highly -- is that we expect your loyalties to be to Australia and Australian interests. You can be proud of your heritage, but your loyalty has to be to Australia, and if that's your position, taking arms in the Syrian civil war is wrong."
