Brig. Gen. Khattab Omer said Saturday that all the attackers were killed or blew themselves up. The area around the provincial headquarters, where the fighting was heaviest, was quiet Saturday morning.
It was not clear how many militants took part in the assault, which appeared to be aimed at diverting attention from the Daesh-held city of Mosul, around 170 kilometers (100 miles) away, where Iraqi forces are waging a major offensive, AP reportd.
Dozens of terrorists targeted four police stations and Kurdish security offices, spreading themselves out through several residential neighborhoods on Friday.
The militants killed 13 workers, including four Iranians, at a power plant north of Kirkuk, and a local television reporter was killed by a sniper in the city.
Kirkuk has been attacked before by Daesh terrorists. Previous attacks have been seen as attempts by Daesh to either capture the city or divert Kurdish troops from the fight in Mosul.