The bombs struck just a few hours after the Ministry of Interior released a statement saying that the violence in Iraq cannot be seen as sectarian in nature because the bombs do not distinguish between Sunnis and Shia.
Two weeks ago, 38 people were killed in a single attack targeting a Sunni mosque in eastern Iraq. Whoever is behind the attacks appears to be targeting different communities in turn, in order to maximise the perception that one attack is in response to the other.
On Monday, one bombing struck the busy commercial area of Sadoun Street in central Baghdad.
One bystander who saw that attack, Zein al-Abidin, said a four-year-old child was among the victims.
Other neighbourhoods targeted included al-Maalif, where six people died, according to the Associated Press news agency.
Deadly blasts were also reported in the eastern New Baghdad area, Sabi al-Boor, Shaab, Hurriya, Bayaa, Sadria, Jisr Diyala, Baladiyat and Madain, about 20km (12 miles) south of the city centre.
No group has said it carried out the attacks, but Sunni militants linked to al-Qaeda have previously used co-ordinated explosions to target Shia Muslims, whom they regard as apostates.
Tensions between the Shia Muslim majority, which leads the government, and minority Sunnis has been growing since last year.
Sunnis have accused the government of Prime Minister Nouri Maliki of discriminating against them – something the government denies.
Mr Maliki has vowed to make immediate changes to Iraq’s security strategy, saying militants “will not be able to return us to the sectarian conflict”.
Monday’s bombings come a week after more than 70 people were killed and many others injured in a series of attacks across the country, in what was described as one of the worst days for sectarian violence in Iraq for several years.
The UN says more than 700 people were killed in April, the highest monthly toll in almost five years.
Estimates put the number of deaths this month at more than 450.