Iraqi police said four of Karim's bodyguards were also wounded in the drive-by shooting.
No other details were immediately available on the killing, the latest in a series of attacks targeting officials linked to Iraq's U.S.-backed interim government.
In other news, at least 15 Iraqis have been reported killed and eight other people injured in a rocket attack near a mosque in the Iraqi city of Tikrit, the hometown of former dictator Saddam Hussein.
The U.S. military said insurgents had fired two rockets in the attack and that one of them had struck near the mosque in northern Tikrit following evening prayers yesterday.
Iraqi interim Prime Minister Iyad Allawi has warned that efforts have entered their "final phase" to peacefully resolve the standoff in Al-Fallujah between Sunni Muslim insurgents and allied U.S. and Iraqi forces.
Allawi said he was still hopeful a solution could be reached without a major military confrontation. But he warned that civilian casualties were likely if he ordered a military solution. "If we cannot [reach a peaceful solution], I have no choice but to secure a military solution. I will do so with a heavy heart, for even with the most careful plan, there will be some loss of innocent lives," Allawi said.
U.S. forces were reported yesterday to have bombarded suspected insurgent positions in Al-Fallujah with artillery and air strikes.
Fighting was also reported in the city Al-Ramadi, where seven Iraqis were reported killed.
(Reuters/AFP/AP)[For the latest news on Iraq, see RFE/RL's webpage on "The New Iraq".]