Al Jazeera's Zeina Khodr, reporting from Baghdad, said those attacks occurred in residential neighbourhoods of the capital.
"[Shula] is a mostly Shia neighbourhood. It used to be a former stronghold of the Mahdi Army, the armed wing of the Sadr movement," our correspondent said, referring to supporters of Moqtada al-Sadr, a Shia leader.
Target not clear
Shula has been a relatively quiet neighbourhood, having not seen been the target of attacks in recent months.
Police said another of the blasts was carried out by a suicide bomber, who detonated explosives on Haifa street in the central Salhiya neighbourhood, near the national museum.
The attacks come as political uncertainty remains following last month's election
Our correspondent said it was not yet clear what the target of that attack was.
"We're getting conflicting reports on the target. Some reports say it was the public works ministry, other reports say he [attacker] blew himself up outside a popular restaurant," she said.
Iyad Allawi, the former prime minister whose coalition won a narrow victory in the country's March 7 poll, sharply criticised the attacks.
"Government officials hold responsibility for not achieving security," Allawi said as he gave blood for the wounded in Baghdad.
"I don't know what they have been doing in these (last) four years."
"They have been saying 'we are ready,'" Allawi said. "Where is this readiness? Nothing is ready."
Tuesday's co-ordinated strike follow similar attacks just two days earlier. On Sunday, three suicide car bombsnear foreign diplomatic missions killed at least 30 people and wounded hundreds more.
In the past five days, four attacks have left more than 100 people dead.
View Al Jazeera's in depth coverage of the Iraqi election
The spate of violent attacks comes as Iraqi politicians continue wranglings to form a coalition government following last month's general elections. No clear winner emerged from the poll.
The Sadr political bloc was expected to announce who it would back for prime minister on Tuesday after holding an unofficial referrendum among its supporters, but said late on Monday night that the decision was being postponed.
Nouri al-Maliki, the incumbent prime minister, is reported to have met the group last night, but no details of any agreement have emerged. The Sadr bloc has in the past indicated it would not support al-Maliki staying on for another term as prime minister.
Our correspondent in Baghdad said a lot of negotiations are taking place, but "no agreements so far, no progress, and there is a real fear that the security situation will deteriorate".
"Over the past few days we've been seeing car bombings, shootings, mortar round being fired, as well as improvised explosive device attacks".