The Montreal MP said Tuesday he'd look at banning semi-automatic weapons, like the military-style, .223-calibre Bushmaster used in last week's massacre.
"There is absolutely no reason that anybody can vote to say that that kind of weapon, that can fire off great numbers of rounds like that, is necessary," Garneau told The Canadian Press.
"That kind of weapon, to me, definitely — well, it is (already) a restricted weapon but one should look at not allowing those things."
Gunman Adam Lanza used a Bushmaster to mow down 20 Grade 1 students at a Newtown, Conn., elementary school last Friday. He also killed six educators and his mother before killing himself.
Garneau noted that almost exactly a year ago, a deranged man attacked students at a primary school in central China. Because he was wielding a knife, not a gun, the carnage was far less —22 children and one adult injured, but no deaths.
"This person had the same kind of intent as the person in Newtown but all of the kids today are still alive."
The Bushmaster is currently a restricted firearm in Canada but it is legal to own one under certain conditions.
A person must be 18 years of age, pass a restricted firearms safety course and obtain a firearms licence and registration certificate. A restricted weapon can be licensed for use in target practice or target shooting competitions or as part of a gun collection.
In limited circumstances, a restricted firearm may be allowed in pursuit of one's occupation or to protect life.
Semi-automatics in Canada are generally restricted to magazines holding only five cartridges.
Several weeks ago, Garneau proposed a four-point plan for tightening gun control in Canada, including further limiting access to assault weapons. He went further Tuesday, suggesting an outright ban.
He said his aim is "putting them out of circulation, not allowing them to be used."
Garneau also said he'd go further than the Harper Conservatives in imposing "very severe" penalties on those who use guns in the commission of crimes.
He'd restrict ownership of guns by people with a history of domestic violence or involvement in gangs and he'd beef up interdiction of firearms flowing illegally across the border from the United States.
Garneau reiterated, however, that he would not revive the Liberal-created long-gun registry, which the Conservative government scrapped earlier this year.
"It was an initiative that had some strong points, in the sense that the police and the RCMP supported it, as did groups representing victims and others," he said.
"But it also had some bad points in that many Canadians, particularly in rural areas, were dead set against it. So it became a very, very divisive issue in this country.
"The Conservatives have killed it and I would not bring it back."
Justin Trudeau, the presumptive front-runner in the leadership contest, has similarly said the gun registry was a failed policy which he would not resurrect.
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