Survivors said a man wearing a "suicide belt" blew himself up on Friday in al-Kadhimain mosque in Abu Dushair district south of Baghdad. At least 31 people were killed and 33 injured in the blast.
However, police sources said they thought rocket-propelled grenades had been fired at Shia who were marking Ashura, an important day in the Muslim calendar.
The US military was not immediately available for comment.
The dead and wounded were taken to al-Yarmuk hospital, one of Baghdad's busiest, where family and friends filled the corridors.
A second blast, apparently caused by a mortar attack, occurred outside the Ali al-Bayya mosque in a predominantly Shia neighbourhood of western Baghdad, killing five people and injuring eight, security sources said.
Speaking to Aljazeera from Baghdad, Walid al-Hilli a key member of al-Daawa Islamic Party said: "These terrorist operations which targeted the Iraqi people attending Ashura procession for the second consecutive year, carry a clear message of killing and violence and preventing stability, security and peace in Iraq."
Police arrest alleged fighters
with plans to attack Shia
Al-Hilli said these groups claimed they wanted to resist foreign forces in Iraq but "in fact they have been killing women, children and unarmed men who came to glorify Allah's rites by visiting [the shrine of] the grandson of the Prophet Muhammad: Imam al-Husain."
Al-Hilli went on to say that "these terrorist groups do not terrorise us".
"Iraqis decided to go on celebrating [Ashura] despite these operations as we can see a huge number of pilgrims flooding to Iraq's holly shrines in Baghdad, Najaf and Karbala and other cities," he added.
Three Iraqis were killed, including a child, and five were injured in an attack that targeted a police centre near the al-Thaqlain mosque in the predominantly Shia neighbourhood of al-Shuala, northwest of Baghdad.
Fears of bombings remain high in
the run up to Ashura
A similar attack killed two policemen and a member of the Iraq National Guard in the mostly Sunni area of Athamiya, police sources said.
Thousands of Shia marched through Baghdad on Friday to mark Ashura, a ceremony commemorating the martyrdom of Imam al-Husain, the grandson of the Prophet Muhammad, in 680CE.
Fears of bombings and other attacks have remained high in the run-up to Ashura, which climaxes on Saturday. Last year, more than 170 people were killed in bombings in Baghdad and Karbala during the ceremony.
US soldiers killed
Separately, three US soldiers were killed in three attacks in and around the northern Iraqi city of Mosul, the US military said.
A car bomb exploded next to a US army patrol in Mosul, killing one soldier and wounding three on Thursday. In a second attack on Thursday, a soldier was shot dead in an exchange of fire. A roadside bomb killed one soldier and wounded another in a third attack on the same day near Tal Afar, about 60km west of Mosul.
The US military also reported the killing of a fourth US soldier in a roadside bomb attack north of Baghdad late on Friday.
Two other US servicemen were injured in the attack, the US military said.
The deaths brought the number of US troops killed since the US-led invasion of Iraq in March 2003 to 1472.
Also on Friday, police found in Karbala the bodies of two police officers, both the sons of the chief of police of Najaf, said Karbala police spokesman Rahman Mushawi. It was not clear who killed the two men.
Their father, Ghalib al-Jazaini, said they had been seized overnight as they drove from Najaf to Karbala for the Ashura activities. Their hands were bound and they had been shot many times in the head.
In northern Iraq, brief clashes broke out between US troops and fighters in Tal Afar, leaving one woman dead and six others wounded, hospital officials said.
Also in northern Iraq, fighters fired six mortar rounds at the governor's office in Mosul. The shells exploded nearby. There was no immediate word on casualties.
In Tikrit, also north of the capital, US-led forces said two fighters were killed and another was wounded trying to plant a roadside bomb. The injured man was arrested and taken to a military hospital.