A Reuters reporter counted at least 20 bodies outside a hospital in the small town of Iskandariya, 40km from the capital. A doctor at the hospital said the toll could be closer to 50.
The Iskandariya hospital's director, Razaq Janabi, said: "Thirty dead have been brought here, I believe that number is rising. I believe it's at 49."
"It was a car (bomb) that was parked outside the station," policeman Sadiq Khudair told Reuters. "It brought down part of the building and the court house."
US occupation troops cordoned off all roads leading to the blast site.
Earlier on Tuesday, a bomber blew himself up outside the house of a US-backed tribal leader in the restive town of Ramadi west of Baghdad, wounding four bodyguards.
The attacks followed a pattern of targeting Iraqis seen as collaborators with the US occupation. Twin bombings in northern Iraq killed more than 100 people on 1 February.
The bombings targeted Iraq's two main Kurdish parties which enjoy good ties to Washington.
Ramadi and neighbouring areas, at the heart of the so-called Sunni triangle where resentment of the United States is strongest, have seen scores of attacks on US forces and allied Iraqis. But areas south of Baghdad, like Iskandariya, have seen much less violence.