At least 18 people were killed and 60 wounded in two separate attacks during the morning rush hour in mainly Shiite areas in the centre of Baghdad, police and medical officials said.
Thursday’s first attack took place in the commercial district of Bab al-Sharj where a bomb went off in a parked car.
Thirteen people died, independent website al-Sumaria News reported.
A bomber, wearing an explosives belt, blew himself up in al-Wathba Square, killing four others.
The casualties included policemen. No one has claimed responsibility for the bombings.
Previous such attacks have been claimed by the radical Sunni Islamic State group, which controls large territory in Iraq’s Sunni heartland in the north and the west.
In recent months, US-backed government troops and allied Shiite paramilitaries have stepped up their fight against Islamic State, which also rules vast areas in neighbouring Syria.