A suicide blast at an outdoor market in the predominantly Shiite northern district of al-Shaab, according to Sky News, killed 38 people and wounded 70, while a car bomb in the southern neighbourhood of al-Rasheed left six dead and 21 injured.
A spokesman for Baghdad Operations Command told state TV a lone attacker set off an explosives vest – at the same time the planted car bomb exploded.
There was no immediate claim of responsibility for the attacks.
Iraq has been currently witnessing a wave of violence since the Islamic State (IS) group took control of parts of Iraq’s northern and western regions in June 2014.
The terror group has intensified its attacks on civilian targets in the face of losing ground to the Iraqi security forces in recent months.
According to the authorities, IS currently controls only 14 percent of Iraqi territory, down from the 40 percent it held in 2014.