General Tom Lawson, chief of Canadian defense staff, identified the slain soldier as Sergeant Andrew Joseph Doiron, whose regiment is in Iraq to train and advise Kurdish forces.
"He was a gifted special operator and a great leader," said Brigadier General Michael Rouleau, head of Canadian Special Operations Forces Command.
"Our thoughts are also with our three injured operators. We will bring Drew home with all dignity and wrap our arms around our injured Brothers and we will carry on with our important mission in Iraq."
Their mission is not to engage in direct ground combat themselves, but they have clashed with IS fighters on at least two occasions.
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In this incident, however, the Canadian military said they were "mistakenly engaged by Iraqi Kurdish forces following their return to an observation post behind the front lines."
"Four Canadian advisers in Bashiqa headed to the front line. On their way back, the peshmerga (forces) did not recognize them, and shot toward them," Iraqi Kurdish security spokesman Halgord Hekmat told AFP.