The deaths came a day after attacks, including nine car bombs in Baghdad, killed 42 people, the latest in a protracted surge of violence that has killed more than 3,300 people already this year, according to an AFP tally.
The deadliest attacks were in Tikrit and Balad, in Salaheddin province north of the capital, where five policemen and a soldier were killed in separate shootings.
In Nineveh province in the north, four bombings left a policeman and a soldier dead.
Violence is running at its highest levels since 2006-7, when an all-out sectarian conflict between Iraq's Shiite majority and Sunni Arab minority killed tens of thousands.
The authorities have blamed a variety of external factors such as the civil war in neighbouring Syria, but diplomats and analysts say the Shiite-led government has not done enough to reach out to disgruntled Sunnis.
Provisional results from last month's election are not expected before May 25, with Prime Minister Nuri al-Maliki seeking a third term in power despite the raging violence.