They attacked government buildings, killing at least six police officers, and a power station under construction, where 13 employees died, officials say.
Twelve IS fighters also reportedly died and fighting seems to be continuing.
Government and Kurdish forces began a long-awaited operation against the IS capital in Iraq, Mosul, on Monday.
Mosul lies 170km (105 miles) to the north-east of Kirkuk, a multi-ethnic city claimed both by Iraq's central government and the Kurds.
Government forces said on Friday they had regained control of a further two villages - al-Awaizat and Nanaha - south of Mosul, evacuating 65 displaced families and killing 15 IS militants.