The violence last evening was the latest in a months-long surge in bloodshed that, coupled with a deadly weeks-long standoff in Anbar province, has sparked fears Iraq is slipping back into the brutal sectarian war that killed tens of thousands in 2006 and 2007.
Car bombs went off in populated civilian areas, both Sunni and Shiite, across the capital, including the Sunni district of Adhamiyah and the mostly Shiite areas of Shaab and Shuala, from about 6:00 pm (1500 GMT) onwards, the officials said.
A gun attack on a police checkpoint on the outskirts of Madain, just south of the capital, left three policemen dead and six wounded.
No group immediately claimed responsibility, but Sunni militants, including those linked to al-Qaeda, often carry out coordinated attacks in and around Baghdad.
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The violence comes as security forces and pro-government tribes are locked in a deadly standoff with militants tied to the al-Qaeda-linked Islamic State of Iraq and the Levant and allied tribes in Anbar, a mostly-desert area west of Baghdad that stretches to the Syrian border.
The unrest comes with parliamentary elections due on April 30. Diplomats, including UN chief Ban Ki-moon, are urging the Shiite-led government to address the "root causes" of the violence and seek political reconciliation with the disaffected Sunni minority.