Brig. Khatab Omar says Brig. Gen. Shirko Fatih was killed as he was leading Kurdish Peshmerga troops in a battle against IS extremists early on Friday outside the city of Kirkuk.
He says at least eight Kurdish Peshmerga fighters were killed during the clashes.
Omar says IS militants attacked the Peshmerga fighters' positions south of Kirkuk, which is located 290 kilometers north of Baghdad.
The casualties come as Iraq is facing its worst crisis since the 2011 withdrawal of U.S. troops, with Islamic State militants now in control of about a third of the country, AP reported.
Iraqi officials say a twin bombing at a crowded market in Baghdad has killed eight people.
Police officials say the Friday morning attack started with a bomb exploding near carts selling used clothes in the city's central Bab al-Sharqi area.
The second explosion, caused by a car bomb, went off two minutes later targeting people who rushed to help the victims from the first blast. Police and hospital officials said along with the eight killed, 20 people were wounded at the market.
All officials spoke on condition of anonymity because they are not authorized to speak to the media.