The Iraqi health ministry and a local hospital in the southern town said 23 people were killed and 58 wounded.
Earlier, occupation forces said 40 were killed and 22 wounded in Saturday's explosions near a mosque in the town 100km south of capital Baghdad. The ruins of ancient Babylon is just outside town.
Polish troops in the area said many among the dead were children.
Initially it was believed that one car bomb had detonated but the military statement said two devices went off.
The blasts occurred about 8:45pm (16:45GMT) in a busy street. Witnesses said the wounded staggered from the scene and sirens wailed as the casualties were ferried to hospital.
Violence has increased in the occupied country in the run-up to the 30 June US transfer of power.
On Sunday three powerful blasts shook central Baghdad. Smoke could be seen rising over the Green Zone, the headquarters of the US occupation force.
The cause of the explosion was not immediately clear and there were no reports on casualties.