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A member of an elite French commando unit was killed on Monday in Iraq while "supporting an Iraqi unit in an anti-terrorist operation", French President Emmanuel Macron's office said on Tuesday.

Sergeant Nicolas Mazier, an air force paratrooper, "fell in combat while carrying out his mission", the Élysée Palace said in a statement, expressing Macron's "profound respect" for his "sacrifice".

It said other soldiers from the unit were also wounded.

An Iraqi security source in northeastern Kirkuk said that Iraqi and French troops were ambushed by Islamic State (IS) group jihadists late on Monday in neighbouring Salah Al-Din province.

In a battle lasting "more than five hours", an unknown number of French troops as well as three members of Iraq's anti-terrorist forces were wounded, the source added.

Mazier is the third French soldier to lose his life this month in Iraq, where the country's troops form part of Operation Inherent Resolve, a years-long campaign by an international coalition against IS.

Two men, Sergeant Baptiste Gauchot and officer Nicolas Latourte, were killed in separate incidents in August, the first in a traffic accident and the second during a training exercise.

Around 600 French troops based across the Levant and Gulf region are involved in Inherent Resolve.