The second car bomb went off in south Kirkuk's Ras Domeez market near a bank, killing five people and wounding 26, he said.
Of the five killed, four were policemen whose patrol was passing by at the time.
"Iraq has no future unless this illegal occupation is ended"
Shafiq, Dhaka, Bangladesh
Send us your views
The mortar attack near the city's civil defence office left one civilian wounded, Salaheddin said, adding that the fourth car bomb targeted a senior officer from Saddam Hussein's former army and destroyed a communication tower but caused no casualties.
All the attacks took place within 30 minutes, with the first car bomb exploding at about 1pm (1000 GMT), Salaheddin said.
Over the past few months, fighters have stepped up attacks in Kirkuk, 250km north of Baghdad, which is a city disputed by Arabs, ethnic Kurds and Turkmen, and violence there is common.
Settling its final status is one of the most sensitive issues in Iraq.