Al-Maliki promised to punish those behind the bombing and linked it to the execution on Monday of Barzan Ibrahim, Saddam's half brother and a former intelligence chief, and Awad Hamed al-Bandar, former head of Iraq's Revolutionary Court.
In a statement released on Tuesday, he said: "When the Iraqi people turned a black page of injustice and dictatorship by giving fair punishment for criminals and mass killers, a desperate group of terrorists and Saddamists targeted an educational center."
The university blast was the fourth bomb attack in Baghdad in the space of a day, following earlier attacks on police and near a Sunni mosque in the Iraqi capital.
In other violence, at least 45 people died in a series of attacks around the capital earlier on Tuesday.
Suicide bomber at university gates
A police source said that the car bomb exploded near the main gate of the university in an area where students wait for minibuses and cars to pick them up to go home.
The suicide bomber then blew himself up near a second gate as people fled.
Hoda Abdel Hamid, Al Jazeera's Iraq correspondent, said: "The university is in a neighbourhood that used to be a mixed neighbourhood, but now it is a Shia neighbourhood ... and some people have said that the university is controlled by the al-Mahdi army, although we have no way of independently confirming this."
The university official said that classes had been cancelled for two days after the attack.
"There is no way people could sit and study. There's glass everywhere and the doors were blown out," the official said.
Police also reported a drive-by shooting in a market in the city's northern al-Bounuk district that killed 10 people and wounded seven.
The US military reported that four US soldiers were killed on Monday by a roadside bomb in northwestern Iraq.
Gulf states back US
The mounting death toll in Iraq comes as foreign ministers from six Gulf Arab states, as well as from Egypt and Jordan, met with Condoleezza Rice, US Secretary of State, in Kuwait.
"Bush's strategy has failed totally in Iraq and USA has already lost the war. The new plan will not work; it will only bring more deaths and make things in Iraq worse..."
Dimos, Hania-Crete, Greece
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Rice is on a regional tour to build support for the commitment by George Bush, the US president, to send 20,000 extra US troops to Iraq.
"We expressed our desire to see the president's plan to reinforce American military presence in Baghdad as a vehicle... to stabilise Baghdad and prevent Iraq sliding into this ugly war, this civil war," said Sheikh Mohammad al-Salem al-Sabah, the Kuwaiti foreign minister, at a joint news conference with Rice.
The US has already won Saudi Arabia's backing for the plan, but the Gulf state said the plan's success depended on Baghdad tackling sectarian strife driving the country towards civil war.
Prince Saud al-Faisal, the Saudi Foreign Minister, said: "We agree fully with the goals set by the new strategy, which in our view are the goals that - if implemented - would solve the problems that face Iraq."
He also said: "Implementation [of the strategy] requires a positive response by the Iraqis themselves... Other countries can help, but the main responsibility in taking decisions rests on the Iraqis."
UN reports on civilian deaths
Meanwhile, the UN reported that more than 34,000 civilians have been killed in violence in Iraq in the last year.
The UN human rights chief in Iraq said that 34,452 civilians had been killed and more than 36,885 wounded in 2006.
|More than 100 people were hurt|
outside the university [AFP]
The day's earlier attacks included a blast from a motorcycle rigged with explosives that left 15 dead and 70 people wounded near a Sunni mosque in central Baghdad, an interior ministry source said.
A roadside bomb targeting a police patrol killed two policemen and two civilians and wounded 10, including three policemen, in Karrada in central Baghdad.
Six people died and 11 were wounded by a bomb inside a car in Sadr City, a Shia district in eastern Baghdad, an interior ministry source said.
And a sniper killed a guard of al-Sabah, a state run newspaper, in northern Baghdad, police said.
The attacks came ahead of a security crackdown in the capital which Nuri al-Maliki, the Iraqi prime minister, has said will be free of political interference.
"The security plan will be away from political interference and will crack down on outlaws," al-Maliki said during a meeting with the United Nations representative in Iraq Ashraf Qazi.
"Those who do not want to be chased by the military should abide by the law," he said.