In the worst attack, a suicide bomber blew up a truck killing 19 people near a police station.
"Firing the gun with one hand randomly to push back civilians, [the bomber] detonated the truck in front of the centre," police said.
Those killed included six women and two children who had gone to see imprisoned relatives as Sunday is visitation day.
Another 6 blasts rocked the city killed eight people.
Three civilians died in an attack on a joint US-Iraqi security patrol.
At least one person was killed in a blast targeting the house of a tribal leader.
A second suicide bomber attacked an Iraqi army checkpoint, while two roadside bombings were reported.
In Baghdad, 34 bodies were found dead after apparent sectarian violence.
Since Tuesday, more than 180 people have been killed in the latest bloodletting.
The northern oil city of Kirkuk has long been a flashpoint in Iraq with its fragile mix of Kurds, Arabs and Turkmen.
Kurds claim the city as their own but this has been resisted by the other communities.
Until recently, violence between the communities was kept to a minimum, partly due to political institutions, including a strong provincial council.
But in the past few months there has been a sharp increase in the number of explosions and car bombs.
US forces in the area attributed the bombing campaign to groups with links to Al-Qaeda seeking to spark civil conflict.
The sectarian bloodshed has increased despite Prime Minister Nuri al-Maliki's repeated pleas for peace.
A massive US-assisted security crackdown in the capital since June 14 has also done little to quell the violence.
At least seven more people died in other rebel attacks reported from across Iraq, including two in Baghdad.
Since the US led invasion of Iraq in March 2003, 2,679 have been killed.
Iraq also stepped up security around churches across the country after a bomb attack on a church in the southern city of Basra on Friday that followed Pope Benedict XVI's criticism of some teachings of the Prophet Mohammed as "evil and inhuman".