Security and medical officials say Islamic State (IS) militants attacked Kurdish forces near the Iraqi city of Kirkuk on January 30, while bombs in Baghdad and Samarra killed at least 21 people.
IS militants launched mortars and attacked positions of Kurdish Peshmerga fighters southwest of Kurdish-controlled Kirkuk.
Officials say a senior Kurdish military commander, General Shirko Fatih, and eight Kurdish fighters were killed in the fighting.
More than 750 Kurdish Peshmerga fighters have been killed in combat since IS overran their defenses in northern Iraq last summer, prompting U.S.-led air strikes.
The Kurds have now regained most of the ground they lost in August.
In Baghdad, at least 18 people were killed when two bombs went off in the Bab al-Sharqi district, which is home to a large market.
In Samarra, about 125 kilometers north of Baghdad, two suicide bombers targeted a security checkpoint in the city center, killing three people and wounding five.
Based on reporting by Reuters and AP