The blasts came a day after a senior American official wrapped up a three-day visit to Iraq to meet with top political leaders to discuss the security crisis in the vast Sunni-dominated western province of Anbar.
The deadliest blast occurred at a bustling bus station in central Baghdad when an explosives-laden car exploded outside the station in the Allawi area, killing at least nine people and wounding 16, a police officer said.
Another parked car bomb targeted a gathering of buses and taxis in Baghdad's northern Hurriyah neighbourhood, killing four civilians and wounding 12 others, the same police officer said.
Two medical officials confirmed the causality figures, which included 16 wounded. All officials spoke on condition of anonymity as they were not authorised to release information.
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The attacks come as Iraqi security forces and allied Sunni tribal militias have been battling al-Qaeda-linked militants in Anbar to recapture strategic territory overrun by militants from the local al-Qaeda franchise, known as the Islamic State in Iraq and the Levant.
Militants and tribal fighters also control part of the provincial capital, Ramadi. Sporadic clashes there and in surrounding areas continue to take place.
Thousands of families have left the area, fearing a government offencive. Clashes between militants and security forces have left at least 60 people dead since violence erupted after the Dec. 28 arrest of a Sunni lawmaker sought on terrorism charges and the dismantling of an anti-government Sunni protest camp in Ramadi.