Thirty-six people died in an attack on a market in the Shia district of Sadr City in Baghdad and eight were killed in an explosion at a nearby town hall. At least 15 more were killed in in Kirkuk in the north of Iraq.
Police said the attack of the Jamila market occurred around 9:15am on Sunday near a police station as residents arrived to shop.
"A car bomb targeted police and civilians at the same time," an officer said, citing an initial report. It was not initially clear whether any security personnel were among the dead.
The powerful explosion shook windows across Baghdad and smoke could be seen rising over the Jamila area of Sadr City.
The market is thronged in the morning by casual workers seeking short-term employment, and is only 50 metres from a police station.
Hours earlier in the same area, US and Iraqi army units raided a series of homes, killing at least one civilian and arresting seven others, police said.
The US military said they were targeting two people believed to be involved in "death squads." Two Iraqi hostages were freed after a battle involving machineguns and grenades. The operation ended before daybreak.
Two weeks ago, a car bomb in the area killed about 60 people.
Police officers and lawyers were among the victims of the blast outside a courthouse in central Kirkuk.
Colonel Tahar Salaheddin of the Kirkuk police said it was not yet known whether the car had been abandoned or whether it was driven to the court by a suicide bomber.
The attacks came the day after Iraq launched a programme of national reconciliation talks.