Two car bombs exploded in a Turkmen Shiite area of Tuz Khurmatu, a town in Salaheddin province, killing three people, wounding 44 and causing extensive damage to 10 houses, police and a doctor said.
And two roadside bombs detonated in a sheep market in the city of Kirkuk, killing two people and wounding 25, other officials said.
Both Tuz Khurmatu and Kirkuk are part of a swathe of territory that Iraq's autonomous Kurdish region wants to incorporate over the strong objections of the federal government - a dispute diplomats and officials say is a major threat to the country's long-term stability.
The bombings came a day after attacks killed more than 60 people across Iraq, which has been hit by a wave of violence in which 371 people have died so far this month, according to a tally of figures given by officials.
Prime Minister Nuri al-Maliki has announced plans to overhaul the country's security strategy and personnel, and that the matter would be discussed at a cabinet meeting on Tuesday.
Violence in Iraq has fallen from its peak in 2006 and 2007 but attacks are still common, killing more than 200 people in each of the first five months of this year, according to AFP figures.