Public Safety Minister Ralph Goodale says there is no known connection between the Toronto shooting suspect and national security concerns, and that the Trudeau government is prepared to consider a proposal to ban handguns.

Still, Mr. Goodale said such changes to handgun provisions would be complex and require a “significant remodeling of the Criminal Code.”

When asked on Tuesday about comments made by Toronto Mayor John Tory in the wake of the deadly Toronto shooting this week, who asked why anyone in the city needs a gun, Mr. Goodale said a similar proposal was first brought forward by people affected by the January 2017 mosque shooting in Quebec City, where six people were killed.

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“A number of groups and organizations made representations to that effect earlier this year. I said that we would be prepared to consider their arguments and we will do that,” Mr. Goodale told reporters on Tuesday.

“We’ll obviously examine carefully what they’ve had to say. Public safety is extremely important to all Canadians and we need to make sure that we get this right.”

Mr. Goodale made the comments alongside former Toronto police chief Bill Blair, who was recently named the Minister of Border Security and Organized Crime Reduction, as the two headed into a set of emergency meetings at the Citizenship and Immigration committee to discuss Ottawa’s response to the growing number of asylum-seekers crossing the Canada-U.S. border.

The public safety minister said at this point in the shooting investigation, which is being handled by Toronto police, there is no known “nexus” between Toronto shooting suspect Faisal Hussain, who killed a 10-year-old girl and an 18-year-old woman and injured 13 others on Danforth Avenue in Toronto on Sunday night, and security agencies. Mr. Hussain also died after exchanging gunfire with police.

Mr. Goodale added that the government’s new firearms bill, which was introduced in March, looks to upgrade the law with respect to background checks. He said he’ll raise the issue of a national requirement to report mental health issues as part of checks when he meets with provincial public safety and justice ministers this fall.

Mr. Blair said the federal government is working with both the province and city to address the issue of gun violence.

He added that he can’t speak specifically about the circumstances that led to the shooting, but Mr. Hussain’s family said the 29-year-old battled psychosis and other mental health issues for years.

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“Unfortunately in our country there are many ways in which a person can illegally acquire a handgun,” Mr. Blair said.

“I am familiar with the way in which people intent on criminal and violent criminal activities can at times obtain handguns both legally and illegally, and overwhelmingly they do it in an illegal fashion.”

In May, the president of Quebec City's Centre culturel Islamique de Québec appealed to a parliamentary committee to include a ban on assault weapons in proposed gun-control legislation.

Six people were killed in a shootout during prayers at the Quebec City mosque on Jan. 29, 2017, and Boufeldja Benabdallah told members of the public-safety committee the death toll could have been much higher if the shooter's weapon had not jammed.

- With a report from The Canadian Press