The latest killings come as the country grapples with months of protests by its Sunni Arab minority, tensions in a swathe of territory that Kurdish leaders want to incorporate into their autonomous region in the north and protracted political deadlock in Baghdad.
Today's deadliest violence struck in the main northern city of Mosul, where a suicide attacker set off a vehicle rigged with explosives near a police patrol on the city's southern outskirts.
And in the ethnically mixed town of Tuz Khurmatu, which lies at the heart of the area disputed between the Kurds and Baghdad, gunmen opened fire on another police patrol, killing three policemen and wounding a fourth, security and medical officials said.
The tract of land, which the Kurds want to incorporate over the objections of Baghdad, stretches from Iraq's eastern border with Iran to its western frontier with Syria.
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Diplomats and officials say the unresolved row is one of the biggest threats to Iraq's long-term stability.
Iraq has suffered an upsurge in violence since the beginning of the year, coinciding with rising discontent among Sunnis that erupted into protests in late December.
Analysts say a failure by the Shiite-led authorities to address the underlying causes of the demonstrations has given militant groups both a recruitment platform and room to manoeuvre.