The incident occurred in Amiriyat al-Falluja in Anbar province — a town more than nine miles, or 15 kilometers, south of city of Falluja.
Security sources said the attackers came from inside the town and were operating as sleeper cells.
Two security officers and two tribal fighters were killed and seven others were injured during the clashes, security sources said.
The fighting is the latest ISIS-claimed strike in a particularly bloody week in Iraq. On Friday, three militants gunned gunned down people in a coffee shop in Balad and killed at least 20 people.
On Thursday, two suicide bombers blew themselves up at a police station in western Baghdad, killing three police officers and injuring 10 others, authorities said.