Iraqi security forces have launched an assault to free students and staff taken hostage by gunmen at the university campus in Ramadi.
Journalists on the scene say special forces are spearheading the assault and reported hearing heavy gunfire.
The action takes place after gunmen from the Islamic State of Iraq and the Levant (ISIL) infiltrated the university earlier on June 7, killed its guards, and then blew up a bridge leading to its main gate.
The Associated Press news agency quoted unnamed police and military officials in Iraq as saying the militants had later withdrawn.
The claim cannot be independently confirmed.
Around 1,000 students managed to escape but an unknown number were captured by the assailants.
The staff and students were reportedly being held inside a dormitory.
Before the military assault began, a student inside the university building told the AFP news agency by telephone that she and other women were ordered to gather in one place.
She told AFP that the leader of the gunmen had addressed them saying: "We will teach you a lesson you will never forget."
Hospital sources in Ramadi said they have received the bodies of two people, one of them a student and the other a policeman.
ISIL and other Sunni-led militants have controlled parts of Ramadi – the capital of Anbar province -- since late December.
The UN's refugee agency, the UNHCR, says the number of people driven from their homes by months of fighting in Anbar province is now close to 480,000.
Due to the ongoing violence was no voting in Anbar in Iraq's parliamentary elections on April 30.
Meanwhile, reports say 59 people were killed in Mosul on June 7 as heavy fighting between government troops and insurgents in the northern city entered its second day.
Police said the dead included 21 troops and 38 militants. Dozens were killed a day earlier.
Iraq is witnessing bloody violence running at its highest level since 2006- 2007, when tens of thousands were killed in a sectarian conflict between the Shi'ite majority and Sunni minority.
According to the United Nations figures, some 900 people were killed in violence across Iraq in May.
With reporting by AP, AFP, Reuters, and the BBC