Peshmerga forces are reclaiming territory previously lost to Islamic State militants, after US fighter jets pounded their positions south of the Kurdish capital Erbil.
The towns of Makhmur and Gwer were retaken by the Kurdish troops, as the US launched its fourth wave of strikes against IS targets.
Kurdish President Massoud Barzani on Sunday requested international military aid to help defeat the militants.
"We are not fighting a terrorist organisation, we are fighting a terrorist state," said Mr Barzani, who was speaking alongside French Foreign Minister Laurent Fabius, in Iraq for talks on the crisis.
"The weapons they possess are more advanced than what the Peshmerga have," he added.
"What we are asking our friends to do is to provide support and to co-operate with us in providing the necessary weapons that would enable us to defeat these terrorist groups," he said.
Mr Fabius said that France would consider supplying equipment to the Kurds.
"One way or another, they must receive equipment that will allow them to defend themselves and to counterattack" Mr Fabius told France 2 television.