General Amir al-Hashimi, brother of Tariq al-Hashimi, and an adviser in the defence ministry, was killed on Monday by unidentified gunmen wearing military uniforms in his home in north Baghdad, Brigadier Qassim al-Moussawi, the government spokesman said.
Further details were not available.
Elsewhere, a car bomber drove into an Iraqi police checkpoint in Tal Afar, 420km northwest of Baghdad, killing one policeman and wounding 12, police Brigadier Najim Abdullah said.
The city was already the scene of a devastating attack on Saturday when a car bomber hit another checkpoint, killing 14 and injuring many more.
Sectarian death squads have killed thousands in recent months, primarily in the capital, and US and Iraqi troops have been carrying out an intensified sweep of the capital to try to root out fighters opposed to the US presence.
At the same time, shootings, bombings and other attacks have been swelling in northern areas, though the bloodshed has not been on the scale seen in Baghdad.