"The cowardly terrorist attacks that occurred today were intending to cover the great success achieved by the security forces through the killing of the leaders of wickedness and terrorism, Abu Omar al-Baghdadi and Abu Ayyub al-Masri," he said in a statement late on Friday.
Al-Maliki announced on April 19 that security forces had killed the two men, one purportedly the leader of al-Qaeda in Iraq and the other the Islamic State of Iraq, in a raid north of Baghdad.
Mike Hanna, Al Jazeera's correspondent in the capital, said four of Friday's attacks were in Shia areas on Baghdad and two of them in Sunni neighbourhoods.
"At this time it would appear that the attacks are being targeted at the civilian population in general, rather than any sectarian basis," he said.
"These attacks represent a warning to the political blocs that they should speed up their efforts to form the government"
a member of Moqtada
al-Sadr's political bloc
"It's impossible at this stage to say whether there is a connection between these killings [of al-Baghdadi and al-Masri] ... and the bombings we are seeing in Baghdad.
"But at this stage it would appear to be an opportunistic attempt to take advantage of the ongoing political uncertainly because there is no agreement about forming a government.
"Iraq had been hoping to celebrate its democratic elections, but at the moment everybody is deeply concerned about this period of instability which it appears is being filled by violent acts," he said.
Iraq held parliamentary elections on March 7, but the country is still waiting for a new government to be formed as no party secured enough seats to govern alone.
Al-Maliki's State of Law bloc and the Iraqiya coalition of Iyad Allawi, a former prime minister, have both been negotiating with smaller parties in an attempt to form a ruling coalition.
Bahaa al-Aaraji, a member of Sadr's political bloc, said Iraq's leaders were more interested in securing their political futures than protecting people.
"Prolonging the time to form the government will pave the way for more attacks," he said.
"These attacks represent a warning to the political blocs that they should speed up their efforts to form the government."
One of the blasts in Sadr City took place as hundreds of worshippers prayed in the streets close to the offices of a Moqtada al-Sadr, a prominent Shia leader.
"I went to see what was going on and to help the wounded worshippers. I saw pieces of human flesh on the ground," Aqil Ibrahim, who was fixing his taxi when he heard the first explosion, said.
|A series of attacks in Khaldiya targeted
police officers and a judge [AFP]
Al-Sadr's so-called Mahdi army militia were urged to guard Shia religious sites following the attack.
"I am confirming that this is a call from Moqtada al-Sadr for the Mahdi army to take responsibility to guard and protect the mosques by cooperating with the security forces," Hazim al-Araji, a Shia leader, said on Sharqiya television.
Three Shia mosques appeared to be among the targets of the attacks.
Elsewhere, at least seven people were killed and 18 others wounded after six roadside bombs exploded in Iraq's western Anbar province.
The bombs went off near the houses of a judge and police officers in the town of Khalidiya, about 83km west of Baghdad.
"Four homes were hit by homemade bombs and C4 [plastic explosive]," Lieutenant Khoder Ahmed al-Alwani, a police officer, said.
An Iraqi soldier was among the dead, killed storming a house filled with explosives after security forces responded to the initial blasts.
Violence in Iraq has fallen in the last two years as the sectarian bloodshed that followed the 2003 US-led invasion faded, but April has been the bloodiest month in the country so far this year.