Most of those killed are students and two guards who were on duty when Al Shabaab militants stormed the university and opened fire indiscriminately.
The Kenya Red Cross says 65 students have been safely rescued from the hostels, although an unknown number of others are still held hostage.
Interior Cabinet Secretary Joseph Nkaissery and police chief Joseph Boinnet are on the ground leading the rescue operation but no official statement has been issued on the death toll. READ: Deaths, injuries in Garissa University Al Shabaab attack.
The Kenya Red Cross says it has dispatched an aircraft to airlift some those injured to Nairobi for specialised treatment.