Seven policemen and four soldiers were killed when IS fighters attacked the police headquarters in the town of Heet, while at least six members of federal forces were killed in an assault on a major army base in Ramadi.
In Heet, a town on the Euphrates about 150 kilometres (95 miles) west of Baghdad, 25 gunmen attacked the police headquarters shortly after midnight.
"They smashed the gates open with suicide car bombs, the 25 men tried to break into the HQ, sparking heavy clashes," police colonel Jabbar al-Nimrawi told AFP.
Nimrawi said the building was now surrounded by police, army, counter-terrorism elite troops and anti-jihadist Sunni tribal forces.
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Doctor Nael Ahmed, from Heet hospital, said seven police officers and four soldiers were killed in the attack and the ensuing clashes.
In Ramadi, less than 100 kilometres (60 miles) west of Baghdad, further down the Euphrates river, a similar suicide unit attacked the 8th Brigade headquarters, just outside the city, on Wednesday.
"They attacked from three directions. They used suicide armoured vehicles to break into the compound, then 13 fighters with suicide vests entered," said senior army officer Awad al-Dulaimi.
A doctor at Ramadi hospital, Ahmed al-Ani, confirmed that he had received the bodies of three members of Iraq's elite counter-terrorism force, including a colonel, and three soldiers.
Some of the last pockets still under government control in the Sunni province of Anbar are in Heet in Ramadi.