Democratic presidential candidates Hillary Clinton and Barack Obama also expressed deep shock.
Ms Clinton said that her "prayers are with the victims and their families, as well as the students, faculty and community devastated by these gruesome killings". Mr Obama said that the US was a "grieving and shocked nation".
The National Rifle Association (NRA), which has been criticised in the past for its attitudes to guns, said that it expressed its "deepest condolences to the families" of those affected at Virginia Tech.
It added: "We will not have further comment until all the facts are known."
The Brady Campaign to Prevent Gun Violence noted that although details were still forthcoming of the shooter's motivations, the availability of guns was an issue.
"It is well known, however, how easy it is for an individual to get powerful weapons in our country," the group said.
"We have now seen another horrible tragedy that will never be forgotten. It is long overdue for us to take some common-sense actions to prevent tragedies like this from continuing to occur."
The male gunman shot himself dead after initially killing two people in a dormitory and then shooting 30 others dead two hours later inside the campus engineering building, Norris Hall.
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