An American soldier also died of wounds sustained in fighting in western Anbar province, the U.S. military said Tuesday.
Three bombs exploded simultaneously near the Interior Ministry buildings in central Baghdad, killing 10 people and wounding eight, police Lt. Bilal Ali Majid said.
A couple of hours later, two roadside bombs ripped through the main Shurja market, also in central Baghdad, killing 10 civilians and wounding 50, police Lt. Mohammed Kheyoun said.
The blasts were the latest sign of the security crisis that prompted U.S. commanders to bolster the American troop presence in the city. More U.S. troops patrolled the streets of the Ghazaliyah neighborhood, a mostly Sunni area and among the most violent parts of the capital.
The violence occurred amid a major U.S. operation to secure Baghdad in order to control Shiite-Sunni sectarian bloodshed that many fear will lead to civil war. The U.S.-Iraqi air and ground attack was launched before dawn Monday in Sadr City, which is controlled by radical Shiite cleric Muqtada al-Sadr and his Mahdi Army militia. Police said three people, including a woman and a child, were killed in the raid, which the U.S. command said was aimed at "individuals involved in punishment and torture cell activities."
Prime Minister Nouri al-Maliki, a Shiite, said he was "very angered and pained" by the operation, warning that it could undermine his efforts toward national reconciliation.
"Reconciliation cannot go hand-in-hand with operations that violate the rights of citizens this way," al-Maliki said in a statement on government television. "This operation used weapons that are unreasonable to detain someone, like using planes."
In other developments:
Also Tuesday, two roadside bombs in Tikrit north of Baghdad killed a policeman, said police Capt. Laith Hamid.
Overnight, nine bullet-riddled bodies were found in Kut south of Baghdad, and four Shiites were shot dead by gunmen in Baqouba, northeast of the capital.
On Monday, President Jalal Talabani, a Kurd, met with the top U.S. commander in Iraq, Gen. George W. Casey Jr., to discuss security operations in Baghdad. Talabani said he told Casey "it is in no one's interest to have a confrontation" with al-Sadr's movement.
The public positions taken by al-Maliki and Talabani signal serious differences between Iraqi politicians and both U.S. and Iraqi military officials on how to restore order and deal with armed groups, many of which have links to political parties.
Speaking to reporters Monday, Casey made no mention of al-Sadr but said he had discussed plans with Talabani to bring "fundamental change to the security situation in Baghdad" before Ramadan, which begins in late September.
Al-Sadr has risen to become a major figure in the Shiite community and a pillar of support for al-Maliki. The prime minister's apology and criticism of the U.S. forces may have helped placate al-Sadr, who on Monday urged his followers to show restraint.
In a statement read at all Mahdi Army offices, al-Sadr urged his militiamen to be "calm and patient, and avoid being drawn into civil war," said the cleric's aide, Mohammed al-Fartousi.
He said al-Sadr urged the militiamen to purge all those who bring the Mahdi Army into disrepute. They should also "denounce the kidnapping of Iraqis, denounce destruction of mosques and denounce killing of innocent people," said his aide, Mohammed al-Fartousi.