The Islamic State of Iraq issued a statement on an extremist website forum saying it carried out the string of car bombings, Site reported.
"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," the statement, posted on Wednesday, said.
Tuesday's attacks were the latest in a series of large-scale bombings and came just as it was announced that national elections would be held in March.
Al-Maliki, who has been running for re-election on a platform of improved security, had previously not asked any senior security officials to step down over lapses.
But he is facing mounting public anger over the attacks and a lack of response could cost him and his party votes.
In a televised address on Wednesday, he appealed for Iraqis to be patient, saying security strategies would be reviewed and further personnel changes possibly made.
He stopped short of saying whether any of his ministers would be held responsible for allowing Tuesday's attacks to occur.
"I call on the Iraqi people for more patience and steadfastness," al-Maliki said in his address.
He also called on 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".
The prime minister was expected to attend a special parliamentary session on Thursday, where MPs have demanded his security ministers answer for lapses that allowed for the attacks.
|The attacks have once again raised questions about Iraqi forces' security readiness to [EPA]
"MPs are angry, and the people are even more angry," Mahmud Othman, an independent Kurdish MP, told the AFP news agency.
"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?"
Suicide bombings at government buildings in August and October left more than 250 people dead.
The group that the government has accused of masterminding Tuesday's bombings, along with the two previous attacks, has also called on security officials to step down.
"He who cannot ensure security for Iraqis should leave," Khudair al-Murshidi, a spokesman for the Baath party, told Al Jazeera from Syria, adding that loyalists to Saddam Hussein's party were not behind any of the attacks.
Roads around Baghdad were reopened on Wednesday after being shut in the wake of Tuesday's attacks but security was beefed up at checkpoints across the city.
Violence continued in and around the capital, however.
In the predominantly Sunni northern district of Adhamiyah on Wednesday, a roadside bomb killed two people and wounded seven while a sniper killed a policeman and a bomb hidden inside a minibus killed two people and wounded 11.
In Mahmudiyah, an ethnically mixed town just south of Baghdad, another bomb concealed inside a minibus killed three people and injured eight.
In his address, al-Maliki blamed Tuesday's co-ordinated attacks on "foreign elements" that backed al-Qaeda and called on Iraq's neighbours - an apparent reference to Syria - to do more to prevent attacks in Iraq.
The US says despite the violence Iraqi leaders are moving the country in the right direction
"I demand of the international community and all countries, including neighbouring countries, who condemn the attacks to turn their words into actions and support the Iraqi people and the Iraqi government by confronting terrorism," al-Maliki said.
Baghdad has previously accused Syria of harbouring senior Baath party loyalists who it says masterminded the attacks in August and October, a claim Syria denies.
A senior Iraqi policeman, meanwhile, said the explosives used in Tuesday's 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," Major-General Jihad al-Jaabiri, the chief of the explosives unit, told reporters.
"Neighbouring countries helped them. The operation required lots of funding, which came from Syria or Saudi Arabia."
Violence across Iraq had dropped dramatically in November, with the 122 deaths recorded being the fewest since the 2003 invasion.
But the Iraqi government and the US military have warned of a rise in attacks in the run-up to the March election.
And while the latest attacks have underlined concerns over the readiness of Iraqi forces to handle security alone when US troops leave, Admiral Mike Mullen, the chairman of the US Joint Chiefs of Staff, has said they will not derail plans to begin withdrawing US troops from Iraq next year.