According to Iraqi media, suicide bombers had attacked police stations and a power station, but that security forces had repelled the assaults.
A news agency affiliated to ISIS claimed its fighters had broken into Kirkuk’s town hall and seized a central hotel.
The attacks come as Iraqi pro-government forces continue an offensive to retake ISIS-held Mosul, to the north.
ISIS militants were reported to have set fire to a chemical plant south of Mosul as they retreated on October 20.
Sources said they started the fire at the sulphur plant in al-Mishraq deliberately when they were being pushed out of the area by security forces.
There are conflicting reports about the scale and extent of the attack on Kirkuk.
A local TV channel broadcast footage of black smoke rising over the city, with automatic gunfire audible.
The Beirut-based newspaper al-Sumaria reported that during the dawn attack, three suicide bombers had blown themselves up.
Kirkuk police sources said three Iranian workers at the power station were killed, along with eight Iraqis.
The city’s governor, Najm al-Din Karim, told the Kurdish news agency, Rudaw, that Kurdish Peshmerga and counter-terrorism forces were completely in control of the situation, and said the attackers were from ISIS sleeper cells.
Security forces had killed six suicide bombers, Najm al-Din Karim added.
Kirkuk, a multi-ethnic city that is located about 180 miles north of the capital Baghdad and 105 miles south-east of Mosul. It is claimed both by Iraq’s central government and by the country’s Kurds.
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