It was the second attempt against Undersecretary Osho Ibrahim.
The latest attack on Ibrahim occurred at 9am on Wednesday when the assailants fired on his motorcade in the al-Ghazaliya district in western Baghdad, police Captain Muhammad Khayun said.
The Justice Ministry said Ibrahim escaped an attack in a nearby area on Tuesday.
Five bodyguards were wounded, Aljazeera has learned.
Claim against troops
A witness at the scene of the shooting on Wednesday, who did not give his name, told Associated Press Television News that the motorcade was attacked by armed men.
The five wounded bodyguards, however, said US troops opened fire on them.
"American troops opened fire on the three-vehicle Land cruiser convoy without any reason," Nasir Bayan said from his hospital bed.
His four colleagues in the same room also said they were attacked by Americans.
A US Bradley fighting vehicle had been seen in the area after the attack, but spokesmen for Task Force Baghdad said they had no information on the incident.