The deadliest attack took place in the Shi'ite district of Habibiya, where 15 people were killed when a car bomb exploded near an open area where cars are displayed for sale.
"The investigation, based on footage from a surveillance camera, showed a man parking a white car and sneaking into a nearby tea kiosk. Five minutes later the car exploded," said police officer Murtatha Abid Ali at the scene of Saturday's explosion, which wounded a further 35 people.
Habibiya is near Sadr City, where more than 70 people were killed in a massive truck bomb blast claimed by Islamic State on Thursday.
Two more people were killed and 7 wounded in a bomb blast targeting vehicle repair shops in Taji to the north of the capital. Other blasts in busy commercial streets and markets in Jisr Diyala, Madaen and Iskan killed seven.
Security forces and militia groups are fighting Islamic State in Anbar province, the sprawling Sunni heartland in western Iraq. In Baghdad, Abadi has proposed sweeping reforms aimed at reducing corruption and patronage, the biggest changes to the political system since the end of U.S. military occupation.
