The statement, translated by SITE on Wednesday, threatened more attacks, saying the latest carnage was the "third wave" in an ISI campaign following bloody days on August 19 and October 25 that left over 100 people dead.
"The list of targets will not end, with permission from Allah, until the flag of monotheism is raised once against on the land of Baghdad and the sharia of Allah rules the land and the worshippers," it said.
The group also claimed responsibility for a suicide bombing in Tikrit, the hometown of executed Iraqi dictator Saddam Hussein, that killed a senior anti-terror officer on December 3.
Maliki earlier ordered the removal of Lieutenant General Abboud Qanbar as enraged MPs demanded answers from the country's leaders over the blasts, which accounted for more dead than the total violent deaths in November, and undermined the government's claims of improved security ahead of March 7 polls.
A senior policeman, meanwhile, said the explosives used in the attacks were manufactured abroad and that the bombers were backed by groups in Syria or Saudi Arabia.
"This material could not have been manufactured in Baghdad, it came from abroad," explosives unit chief Major General Jihad al-Jaabiri told reporters.
"Neighbouring countries helped them. The operation required lots of funding, which came from Syria or Saudi Arabia."
Security was beefed up at checkpoints across Baghdad, although roads were reopened after being shut in the wake of the five coordinated attacks.
Maliki, who has been sharply criticised by politicians since the bombings, appealed for unity among Iraqi leaders.
"I call (on all politicians)... to avoid using these disasters to create conflicts during the election campaign because if the temple falls, it falls on everyone, and no one will be spared," he said in a televised address.
Yet lawmakers demanded that Maliki and his ministers answer for any failings that led to the attacks.
"MPs are angry, and the people are even more angry," influential independent Kurdish MP Mahmud Othman told AFP.
"We want to know what is going on. What is the security plan? Have they revised the plans since the explosions in August and October? What are the results of their investigations?
"Why do these explosions keep happening?"
Another spate of deadly attacks rocked the capital Wednesday as a roadside bomb in the predominantly Sunni northern Baghdad district of Adhamiyah killed two people and wounded seven, according to an interior ministry official.
Also in Adhamiyah, a sniper killed a policeman and a bomb hidden inside a minibus exploded, killing two people and wounding 11.
In Mahmudiyah, an ethnically mixed town just south of Baghdad, another bomb concealed inside a minibus killed three people and injured eight.
Tuesday morning's bombs all exploded within minutes of each other.
One suicide attacker detonated his payload at a finance ministry office, another struck at a tunnel leading to the labour ministry and a third drove a four-wheel-drive car into a courthouse.
A fourth in a car struck a police patrol in Dora in south Baghdad, while a car bomb hit interior ministry offices in the city centre.
Maliki called the attacks a "cowardly" attempt "to cause chaos... and hinder the election," and said they were deliberately timed to come after MPs agreed on a new electoral law on Sunday.
In August and October, Al-Qaeda carried out bloody coordinated vehicle bombings against government buildings in Baghdad, puncturing confidence in the security forces.
Violence across Iraq dropped dramatically last month, with the fewest deaths in attacks recorded since the 2003 invasion. Official figures showed a total of 122 people were killed in November.
Both the Baghdad government and the US military have warned of a rise in attacks in the run-up to the election.
US forces remain on track to begin withdrawing from Iraq in large numbers next year, said Admiral Michael Mullen, the chairman of the Joint Chiefs of Staff.
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