Higher Education Minister Abed Dhiab al-Ujaili, said some 75 hostages 40 of them his ministry's staff were in captivity after the raid by militiamen wearing police-style uniforms.
"Those who were set free told us that a few of the hostages have been killed, while most of them were tortured," he told AFP. "I'm very much concerned about their welfare," he said of the remaining hostages.
Ujaili's comments came as the sectarian violence in the capital showed no let-up.
Gunmen stormed a bakery in the mixed Zayuniyah neighbourhood and killed nine workers in the latest attack by insurgents on a trade that has traditionally been carried out by the majority community.
Fifteen other civilians were killed in Iraq, including 10 in shootings in Baquba, north of the capital.
Ujaili said he was stepping down from the government until it secures the release of all hostages and takes action against militias suspected of infiltrating the security forces to carry out kidnappings and murders.
"I am stepping down until something has been taken actively, there's not just talking," he told BBC radio. "The police force should be investigated and should put the right people in the right place."
Asked if he felt there was currently no effective government in Iraq, Ujaili replied: "That's right, I feel, yeah, there is no effective government."
Embattled Prime Minister Nuri al-Maliki, on a visit to neighbouring Turkey, promised minor changes in the government and steps to rein in the violence.
"There is work under way on that at the moment," he told reporters when asked about a possible government reshuffle. "There will be no fundamental changes, but only very minor ones soon."
"A package of measures to be enacted in the coming days is on the agenda in order to stop the blasts and the bombings," Maliki said. "We will not allow certain groups to be settling accounts between themselves."
On Wednesday, government spokesman Ali al-Dabbagh played down the mass abduction of higher education ministry staff and visitors, insisting that only 39 people had been abducted, of whom just two were still being held.
The blow to the hard-won Sunni representation in Iraq's national unity government came as the United States also piled on the pressure for more effective action against the militias.
The top US commander in the Middle East, General John Abizaid, revealed that he had pressed Maliki to disband the militias "very soon" just a day before the mass kidnapping.
"He must disband the Shia militia," Abizaid told a Senate committee on Wednesday, referring to Maliki.
Abizaid warned that US and Iraqi forces have four to six months to reduce the levels of sectarian violence before the conflict tips into all-out civil war.
A freed hostage and an eyewitness told AFP that the carloads of militiamen who carried out Tuesday's mass abduction were in police uniforms.
The witness said she saw gunmen wearing police commando uniforms handcuff the hostages. "They brought all the men into the parking lot, took their car keys and loaded them in the cars and drove off," she said.
A university professor who was briefly kidnapped said the gunmen first seized their captives' mobile phones.
"They also stripped the (building's) guards of their weapons. After that they put us all in one place and started blindfolding us," before leading the hostages at gunpoint to waiting cars.
He said the hostages were later bundled into a hall and questioned for a long time, before he was set free and warned not to talk about his ordeal.
US National Security Advisor Stephen Hadley confirmed that a formal review was under way of US Iraq policy. It had been launched "fairly discreetly" several weeks ago, he said.
On Thursday the London daily Guardian, citing sources familiar with the Bush administration, said that a four-point strategy was being worked out for victory in Iraq.
It said that as part of this, Bush wanted one last big push on Iraq by sending 20,000 more troops to the war-ravaged country. An international conference on Iraq was also being considered, it said.
Senior State Department official David Satterfield said the US was ready "in principle" for direct talks with Iran on its role in Iraq.
"We are prepared, in principle, for a direct dialogue with Iran. The timing of that dialogue is one that we are considering," Satterfield told the Senate committee.

Copyright AFP (Agence France-Presse), 2006