The offensive began at dawn on Sunday, backed by air strikes from the US-led coalition battling ISIS.
Kurdish and Iraqi government forces have been encircling Mosul ahead of an offensive to take the city itself.
A Kurdish commander said more than five thousand troops were involved in the latest operation.
The militants reportedly responded to the air strikes by trying to ram explosive-packed vehicles into Kurdish lines.
The city which is Iraq’s second largest city, has been under IS control since June 2014.
