The top US commander in the Middle East, General John Abizaid revealed he had pressed Maliki to disband the militias "very soon" the day before Tuesday's audacious daylight raid in which dozens of hostages were seized by gunmen in security force uniforms in the capital.
Officials differed sharply over the number of hostages still held, and how many had been seized in the first place.
Government spokesman Ali al-Dabbagh said only 39 people had been abducted, all but two of whom had been released.
But Higher Education Minister Abed Dhiab al-Ujaili said 40 of his staff were still held captive after what he described as a "sectarian attack" and announced that he was halting his duties until they had been freed.
"I suspect it is sectarian, definitely, but the people who have been kidnapped are from all groups," Ujaili told CNN.
Maliki slammed the kidnappers as "worse than extremists" for targeting "scientific professionals who are dedicating their lives for the country".
"I do not need only the captives to be released, but I also want those who did that act," the prime minister said at Baghdad university during a visit to calm shocked professors and students.
Witness reports that Tuesday's raid was carried out by militiamen in military-style uniforms raised renewed accusations from the Arab minority of security force collusion with the militias.
"This cowardly act confirms what we have always warned and we blame the government and the interior ministry for this crime," said Iraq's leading Sunni clerics' organisation, the Muslim Scholars' Association.
The authorities have already detained five police commanders in connection with the abductions, and the higher education minister said Maliki seemed to have taken a decision to crack down on the militias.
"But I am awaiting the outcome. I want to see the results," Ujaili said.
The coalition's outgoing commander for the Baghdad region, Major General James Thurman, voiced confidence that the interior ministry was taking strong action to track down the kidnappers.
"I think the minister of interior -- I talked to him five times yesterday about that -- he was very upset and we worked that operation all night and ran several tips that we actioned on and I've seen his determination," Thurman said.
Abizaid, the head of the US Central Command, told a Senate committee that US and Iraqi forces have four to six months to get the levels of sectarian violence down before it tips into civil war.
"He must disband the Shia militia," Abizaid said, referring to the prime minister.
The US commander said he did not believe that boosting the current 144,000-strong US force in Iraq was the way to tackle the sectarian violence but added that he did not recommend a draw down either.
"No, I do not believe that more American troops right now is the solution to the problem," he told the Senate committee.
"Under current circumstances, I would not recommend troop withdrawals," he added.
However National Security Advisor Stephen Hadley confirmed that a formal review was under way on Iraq policy within the US administration.
The review had been launched "fairly discreetly" several weeks ago, he said.
And senior State Department official David Satterfield revealed that as part of the review the United States 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.
In other violence on the ground on Wednesday, at least 22 people were killed, 15 of them in two car bombs in the capital.
Police also found 73 bullet-riddled corpses, 55 of them in Baghdad.
The US military announced the deaths of six troops bringing its losses since the March 2003 invasion to 2,854, according to an AFP count based on Pentagon figures.

Copyright AFP (Agence France-Presse), 2006