The group, called the Islamic State of Iraq, posted a message on a website confirming it carried out the Sunday attacks, Xinhua reported.
The attacks were in response "to what the Shiite-led government does, from raids, arrests, displacement and humiliation to seizing the lands and properties of Sunni neighborhoods," the statement said.
Marketplaces and parking lots in Shiite districts in eastern Baghdad were hit with car and roadside bombs in the simultaneous attacks.
People in Sunni Arab provinces in Iraq have protested in recent weeks against the Shiite central government. They say Shiite-dominated security forces have indiscriminately arrested and tortured Sunnis.
Iraqi Prime Minister Nouri al-Maliki has attempted to calm the unrest by offering to released hundreds of Sunni detainees. He has also raised salaries of Sunni militia members and lifted a ban on some members of the Baath party, once the political base of Saddam Hussein, the dictator who was executed in 2006.