The toll was expected to rise.
Tensions have increased in recent months between Kirkuk's Kurdish and Arab populations as Kurds seek to absorb the city into their autonomous region despite opposition from the city's Arab and Turkmen residents.
Meanwhile, south of the Iraqi capital of Baghdad, the US military launched a new offensive, as part of its "surge" of 28,000 new American troops sent to Iraq this year.
For the past month, US and Iraqi forces have been waging offensives in the region southeast of Baghdad and in the city of Baqouba, 60km to the northeast.
US troops have also recently stepped-up a security sweep in Baghdad, hoping to bring calm to the capital and boost the government of Nuri al-Maliki, the Iraqi prime minister.
The military said in a statement that the new sweep "aimed at preventing the movement of weapons, munitions and insurgents into Baghdad".
But violence in the capital has continued, with a string of attacks on Monday morning killing at least nine people.
In the deadliest of those attacks, a roadside bomb exploded as an Iraqi army patrol passed in the Boub al-Sham area on the city's northeast outskirts, killing five soldiers and wounding nine others, an army officer said.