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One report said some guards had been killed at the Anbar University campus.
Parts of Ramadi have been under their control for months.
Security forces have sealed off the campus.
The staff and students are reportedly being held in a dormitory.
The violence in Anbar meant there was no voting there in the 30 April parliamentary elections.
Prime Minister Nouri Maliki’s alliance won the elections, but fell short of a majority.
Mr Maliki wants a third term, but other parties have voiced strong opposition.
The army said some 80 insurgents died.
