In the first attack on July 2, a suicide car bomb exploded near a restaurant and shopping area in the central district of Karrada.
The street was busy with shoppers after sundown in the holy month of Ramadan.
A second bomb exploded later in a predominantly Shia area north of the capital.
The bombings come a week after Iraqi security forces recaptured the city of Falluja from Islamic State militants.
Authorities say the city was used as a launching pad for attacks on Baghdad by ISIS.
On July 2, ISIS claimed responsibility for the suicide car bomb in Karrada, which caused a huge street fire on the main street, in a statement distributed online by supporters of the hardline Sunni group.
The car bomb went off as people were eating out late during the Muslim fasting month of Ramadan, which ends next week.
ISIS still controls large swathes of territory in the country’s north and west, including Mosul, Iraq’s second largest city.
However, ISIS has been under pressure in Iraq and in neighboring Syria, where it has been targeted by government forces and US-backed rebels.
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