Provincial officials said at least 30 Shia pilgrims died in a suicide attack near the city of Nasiriya.
Earlier, Iraq's Interior Ministry said at least 24 people were killed in blasts in Shia areas of Baghdad.
The attacks come amid a rise in sectarian tensions after the last US combat troops withdrew in December.
The head of the provincial council in Nasiriya, Qusay al-Abadi, said at least 30 pilgrims were killed and more than 70 injured in the attack near Nasiriya. AFP quoted the official Dhi Qar provincial website as saying the pilgrims were walking to the holy city of Karbala.
The BBC's Rafid Jabboori in Baghdad says Iraq is going through a severe political crisis and the situation in the country is tense.
The Baghdad attacks occurred during the city's rush hour and the Interior Ministry says they targeted gatherings in of civilians in the Sadr City and Kadhimiya areas and injured at least 66 other people.
Unnamed officials told the AFP news agency that between 14 and 15 people had been killed when two car bombs exploded simultaneously in Kadhimiya at around 09:00 (06:00 GMT). The Associated Press (AP) said 15 people died in the blasts.
Recent attacks in Iraq
- 5 January - At least 24 die in blasts in two Shia areas of Baghdad. A roadside bomb kills 30 pilgrims near Nasiriya
- 4 January - At least three die in bombings and grenade attacks in Baquba and Abu Ghraib, north of Baghdad
- 26 December - At least seven killed in suicide car bomb attack outside Iraq's interior ministry
- 22 December - 68 killed in multiple blasts in Baghdad
- 5 December - At least 30 killed in attacks targeting Shia pilgrims in central Iraq
- 27 October - 38 killed, 78 injured in twin bomb blasts in a Shia area of Baghdad
- 12 October - 28 killed by car bombs and roadside bombs around Baghdad
- 15 August - At least 60 killed in co-ordinated attacks in several Iraqi cities
It quoted anonymous hospital officials as saying that 30 minutes later a roadside bomb exploded near a tea shop, killing one. AFP quoted security officials as saying nine people were killed and 35 wounded in the Sadr City attacks. Reuters put the toll at 10.
"There was a group of day labourers gathered, waiting to be hired for work. Someone brought his small motorcycle and parked it nearby. A few minutes later it blew up, killed some people, wounded others and burned some cars," a police officer told Reuters at the scene of the first attack.
Iraq's power-sharing government has been in crisis since an arrest warrant was issued for Sunni Vice-President Tariq al-Hashemi on terror charges two weeks ago. He has denied the accusations against him.
The al-Iraqiyya group, the main Sunni bloc in parliament, is boycotting the assembly in protest. It accuses Prime Minister Nouri Maliki, a Shia, of monopolising power.
Mr Hashemi is currently in Irbil in Iraqi Kurdistan, under the protection of the regional government, but Mr Maliki has demanded that they give him up.
"Political leaders fight each other for power, and we pay the price," Labourer Ahmed Khalaf told AFP at the site of one of the Sadr City explosions. "How is it our fault if al-Hashemi is wanted, or someone else is wanted?" he asked. "Why should we pay instead of them?"