Education officials have rejected government claims that most of the hostages have been freed, saying dozens are still missing. They blamed Shia militias for abducting them.
Iraq's interior minister, a Shia, said that the attack on the Sunni-run higher education ministry was not sectarian.
Meanwhile, US-led forces raided Baghdad's mainly Shia Sadr City for the second time in two days, searching for the men suspected of carrying out the mass kidnapping.
British and Iraqi forces also raided homes in southern Iraq on Monday and arrested four men suspected of being involved in the kidnapping of four American security guards and their Austrian colleague, an official said.
Iraqi society was dealt another blow on Monday when gunmen assassinated a prominent comedian.
Walid Hassan, whose satirical television show made fun of the US-led forces, sectarian militias and the government, was shot three times in the head while on his way to work.
He was the latest of dozens of Iraqi broadcasters and journalists to be killed.
"We feel we're all at risk," a journalist at Al-Sharqiyah TV said. "We all think of quitting the station."
Several senior Shia members of the government were also attacke on Monday - apparently by members of Sunni armed groups.
Mohammed Abbas Auraibi, the minister of state and a member of Iraq's Shia majority, said a roadside bomb hit his convoy on Monday morning on a highway in eastern Baghdad, wounding two of his bodyguards.
"I was returning from an official visit to Amarah when our convoy was attacked," he said in an interview with The Associated Press news agency.
"Thank God the two guards were only slightly injured."
Hakim al-Zamily, a Shia deputy health minister, also escaped unhurt when gunmen opened fire on his convoy in Baghdad.
"The convoy was blocked by several cars and we were fired on from the cars and round about," al-Zamily told Reuters news agency.
"Two of my guards were killed, but we were able to fight our way out."
The attacks came one day after another deputy health minister, Ammar al-Saffar, also a Shia, was abducted from his home in northern Baghdad.
Officials said the al-Saffar was taken away by men who wore police uniforms and arrived in seven vehicles.
Al-Saffar was believed to be the most senior government official kidnapped in Iraq since the war began in March 2003.