Thirty-two people have reportedly been killed and more than two dozen others injured during a shooting rampage this morning at Virginia Tech, making it the deadliest killing spree in U.S. history, according to law enforcement sources.

The unidentified shooter was among the dead, according to officials, who also said that several were injured in the shootings, at West Ambler Johnston, a dormitory, and Norris Hall, which houses the College of Engineering. Authorities said the first shooting was reported shortly after 7 a.m.

"We have a ballpark figure on fatalities," Virginia Tech Police Chief Wendell Flinchum, said at a news conference broadcast earlier today by CNN. "It's at least 20 fatalities."

Flinchum said he did not know whether the shooter was a student. Some of those killed were students in a classroom at Norris Hall, he said.