The US military blamed an accident on a gas main for the disaster,
But Iraqi authorities insisted insurgents had fired rockets into the largely Shiite district of Zafaraniyah and had detonated at least two bombs.
A little known Sunni insurgent group claimed responsibility in a statement on an Internet site that could not be authenticated.
The same group had claimed responsibility for a suicide bombing on Thursday that killed 35 people near one of Shiite Islam's holiest shrines in Najaf.
Political tensions
Whatever the real cause of the latest blasts, the carnage increased political tensions in the war-torn Iraqi capital, as Prime Minister Nuri al-Maliki blamed Sunni extremists for "this ugly crime".
Major General William Caldwell, chief spokesman for US-led forces in Iraq, told reporters that American explosives experts believed a major gas explosion had triggered the blasts.
The US position differed completely from that of the Iraqi government.
"Our information was based on a report given to us by the interior ministry," said Ali Hussein, an official in the media relations department of the Council of Ministers office, part of Mr Maliki's government.
"There were three explosions. The first was a Katyusha rocket fired at a market. Then a car bomb exploded 100 metres away from the first explosion," he said.
Mr Maliki accused Sunni extremists aiming to ignite civil war.
"We strongly condemn the series of terrorist attacks which were carried out by takfiri (hardline Sunni) terrorists on Sunday, which killed dozens of people," the Shiite premier said in a statement.
The carnage led to supporters of the radical anti-American Shiite cleric Moqtada al-Sadr demand the formation of armed self-defence units.
Car bomb
Meanwhile a car bomb has exploded on a bridge south-east of Baghdad, killing five people and damaging the bridge.
The bomb went off around 9pm on Diyala Bridge, 20 kilometres southeast of Baghdad, said Captain Ali Mahdi.
Five people survived the blast but died of injuries after they reached the hospital, he said.
The bridge, which is over a small river that joins the Tigris, is one of the links between Baghdad and the southern province of Wasit. It was not clear if the bridge will be closed due to the damage.
Authorities have said that insurgents have repeatedly targeted the roads south of Baghdad recently in an attempt to sever the capital from southern cities.
Baghdad is in the grip of a dirty war between rival sectarian gangs and insurgents targeting US-led forces and Mr Maliki's government.