The Islamic State jihadist group claimed an attack in the Baghdad Jadida neighbourhood in the east of the city, saying it was carried out by a man wearing an explosive vest.
Officials said at least eight people were killed and at least 29 wounded in Baghdad Jadida, although some said the area was hit by a roadside bomb as well as a suicide bomber.
Conflicting accounts are common in the confused aftermath of attacks in Iraq: police at the scene said it was hit by a roadside bomb that wounded six people but left no fatalities.
Another suicide bomber targeted the Bayaa area in south Baghdad, killing at least nine people and wounding at least 26, officials said.
There was no immediate claim of responsibility for that attack, but IS frequently carries out suicide bombers targeting Iraqi Shiite Muslims, whom it considers to be heretics.
Tuesday’s violence came two days after another suicide bombing claimed by IS killed six people in western Baghdad.
A day before that, bomb and gun attacks claimed by the jihadist group killed 12 people in the area of Tikrit, a city north of the capital.
Iraqi forces are preparing for a push on Mosul, the last IS-held city in the country, after regaining much of the Iraqi territory the jihadists seized in June 2014.
But IS has maintained the ability to carry out attacks in government-controlled areas even as the jihadist group lost ground, and it is likely to increasingly turn to such insurgent tactics if it loses Mosul.