Security and medical sources said both incidents took place in the northern province of Salahuddin on Sunday.
In the first incident, a group of militants attacked a police station near a stadium in the town of Tuz Khormato, shooting dead six policemen.
In the town of Baiji, Iraqi security forces found the decapitated heads of three men in a market during the early hours of Sunday.
The men, including an anti-Qaeda leader, were kidnapped on February 6 near the provincial capital city of Tikrit.
Fatal bombings and shooting attacks continue to claim more lives in Iraq.
On February 7, over a dozen people were killed in such attacks that hit northern Iraq as well as the capital, Baghdad.
The attackers in Iraq often target crowded places, including markets, cafés and mosques, in an attempt to cause maximum fatalities.
According to figures compiled by Iraq’s ministries of health, interior and defense, some 1,013 people were killed in January alone, making it the deadliest month since April 2008.
Iraqi Prime Minister Nouri al-Maliki says al-Qaeda terrorist group is behind the killing of thousands of people in his country.
The premier blames the group for “destroying the houses of citizens and killing them, and blowing up government departments.”