However, school President Charles Steger says police have still not confirmed that the same person was responsible for two killings earlier at a dormitory building on the campus.
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Police have not given a motive for the attacks.
The university in the eastern U.S. state of Virginia is closed Tuesday. Students, faculty, community members and political leaders including President Bush will gather later for a prayer meeting to mourn the 33 deaths from what is being called the worst shooting incident in the United States.
Some Virginia Tech students and their parents are expressing anger over the failure of officials at the university to warn students and lock down the campus immediately after the first dormitory shootings.
Among the dead were an engineering professor from India and an Israeli lecturer.
Witnesses described horrific scenes as the gunman calmly fired into groups of students huddled behind desks.
The gunman killed himself before police arrived.
Virginia Tech is a state university with about 26,000 students. It is located in the southwest corner of the state, about 386 kilometers from Washington, D.C.
The university's web site says that more than 1,400 international students are enrolled at Virginia Tech in any given year.
Some information for this report was provided by AFP and Reuters.