One blast hit a car park across the street from Yarmuk hospital in the west of the Iraqi capital, killing at least four people and wounding 10.
The second struck a residential area in Mahmudiyah, south of Baghdad, killing at least four people and wounding at least 13.
Bombings and shootings in the capital were once a daily occurrence, but have declined since the Islamic State group spearheaded a sweeping offensive last June and overran large areas north and west of the city.
That has tied them down in fighting outside the capital that distracts from their ability to carry out attacks against civilians in Baghdad.
Another two people were killed the same day by a roadside bomb in Taji, just north of the capital, he said.