Two people were shot dead in a university dormitory in the town of Blacksburg early on Monday morning before another 30 people were killed when a gunman rampaged through a classroom building across campus two hours later.
Police said they were still investigating the shooting at the dormitory when they got word of gunfire at the second building.
They arrived to find the doors to the building chained shut from the inside. They forced their way in and followed the sound of gunshots to the second floor where they found that the attacker had killed himself.
Steger said the attacks were "two very tragic events" that "may or may not" be related.
"We just don't know at this point in time."
The Chicago Sun Times newspaper cited an unnamed official source as saying that authorities were investigating whether the gunman was a Chinese man who arrived to the US last August on a student visa issued in Shanghai.
Witnesses described him as Asian, wearing a brown hiking shirt and black combat-style vest.
'Kept in the dark'
Students said there had been no public-address announcements or other warnings on campus after the first attack until an email was sent around the time of the second shooting.
Andrew Capers Thompson, a 22-year-old graduate student, said: "We were kept in the dark a lot about exactly what was going on."
December 1989 - Marc Lepine shot dead 14 women in Montreal's Ecole Polytechnique.
August 1966 - Charles Whitman climbed to the 28th-floor observation deck of a clock tower and opened fire at the University of Texas, killing 16 people before police killed him.
March 1996 - Thomas Hamilton killed 16 children and their teacher at a school in Dunblane in Scotland.
March 1997 - Mohammad Ahman al-Naziri killed six children and two staff during attacks on two schools in Sanaa, Yemen.
April 1999 - Two students killed 12 students and a teacher at Columbine High School in the United States.
February 2002 - A former student thrown out of trade school shot dead three people in Freising, Germany
April 2002 - Eighteen people died when a former student opened fire at a high school in Erfurt, Germany after being expelled.
October 2006 - A man killed five girls and wounded seven before killing himself in an Amish school in Pennsylvania, US.
Wendell Flinchum, the Virginia Tech campus police chief, said the first shooting had appeared to be "domestic in nature" so authorities did not feel that the campus needed to be closed.
"We had information that led us to believe that the building was secure and that the person had left the building," Flinchum told reporters. "We acted on the best information we had at the time."
He said the university had sent people to knock on doors to spread the word as well as sending the email, but it was difficult to reach everyone arriving on the campus.
Police said that over the past two weeks there had been bomb threats on the campus, which is attended by more than 25,000 full-time students, but had not established links between the bomb alerts and the shootings.
A memorial service and a candlelight vigil are planned for Monday. Flags will hang at half-mast across the state.
It is the second time in less than a year that the Virginia Tech campus has been closed because of a shooting.
In August last year, opening day classes were cancelled and the campus closed when an escaped prisoner allegedly killed a hospital guard off campus and fled to the Tech area.