Both attacks were carried out by bombers on foot, wearing explosives-laden vests, two police officers said. One bomber struck in Baghdad's Bab al-Sharji area, killing nine civilians and three police officers there. Forty-five people were wounded in that explosion.
The second bomber hit in al-Wathba Square, killing nine people, including four policemen, and wounding 31, AP reported.
Two medical officials confirmed the casualty figures. All officials spoke on condition of anonymity because they are not authorized to talk to reporters.
The ISIL terrorist group has claimed responsibility for the attacks in the mainly Shiite districts in central Baghdad.
In a statement posted online, the Takfiri group said two of its members wearing explosive vests had targeted police and militia fighters.
Iraq is going through its worst crisis since the 2011 withdrawal of US troops. ISIL controls large swaths of the country's north and west after capturing Iraq's second-largest city of Mosul and the majority of the western Anbar province last year.
Following its blitz last year, ISIL now holds about a third of Iraq and neighboring Syria in its self-declared "caliphate".
Since the emergence of the ISIL extremists, Baghdad has seen near-daily attacks, with roadside bombs, suicide blasts and assassinations targeting Iraqi forces and government officials, with significant casualties among the civilian population.
The violence has killed hundreds and displaced tens of thousands of Iraqis.