The assault on Wednesday came in Hawijah, a Sunni Arab town in ethnically mixed Kirkuk province near which security forces stormed an anti-government protest camp in April, triggering Iraq's deadliest day this year.
One suicide bomber detonated an explosives-rigged vehicle near a police station, while a second blew up another near a local administrative building.
Militants then hit both buildings and a local council office with mortar fire, and gunmen clashed with the army.
Seven civilians, three soldiers and four militants were killed and 22 people wounded, army Staff Major General Mohammed Khalaf al-Dulaimi said.
Troops were combing the area for another nine assailants who were believed to have escaped, Dulaimi added.
The Hawijah assault came a day after militants attacked two police stations and a local official's house in two towns northwest of Baghdad, killing seven police and the official's brother.
In the capital, six members of a single family were shot dead on Wednesday, officials said.
A man, his wife, their three children aged between three and six, and another woman were killed in the Shaab area of east Baghdad, officials said.
North of Baghdad, gunmen killed two farmers in the Muqdadiyah area and a soldier in Taji. One person was also shot dead in the northern city of Mosul.
Prime Minister Nuri al-Maliki said in speech on Wednesday that there has been "killing by identity card and name", referring to the selection of victims on the basis of the confessional or ethnic affiliation given away by their family or given name.
There are persistent fears that Iraq will return to the all-out Sunni-Shiite sectarian violence that peaked in 2006-2007 and killed tens of thousands of people.
The UN refugee agency said on Tuesday that it was "increasingly concerned about the situation in Iraq, where recent waves of sectarian violence threaten to spark new internal displacement of Iraqis fleeing bombings and other attacks."
With the latest violence, more than 660 people have been killed this month and over 4,450 since the beginning of the year, according to AFP figures based on security and medical sources.
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