Police sources said more than 100 people were wounded during the near-simultaneous strikes on Thursday evening and the death toll was expected to rise as bodies were pulled from the rubble.
"Buildings have been flattened... and there are still people trapped," a police officer said, adding that a final death toll was unlikely to be known until daylight.
Iraqi police and medics said car bombs and mortar strikes were responsible for some of the attacks.
The attacks came soon after Nuri al-Maliki, the Iraqi prime minister, said Iraqi forces were ready to assume security responsibility for a second province in the south of the country.
"This makes us optimistic and proud because we managed to fulfil our promise," al-Maliki said.
Speaking after a cabinet meeting, al-Maliki said Iraqi forces will assume control of Dhi Qar province in September.
The Iraqis took over Muthanna province in the south from Britain in July.
The attacks came as George Bush, the US president, began a round of pre-election speeches urging Americans to back continued US military operations in Iraq.
Thursday's violence came one day after another deadly bombing in a central Baghdad market, part of a violent week that has seen hundreds of Iraqis killed amid fears the country is heading towards civil war.