TORONTO — Canadian investigators said Tuesday there was no link to terrorism in the mass shooting that killed two people and wounded 13 as they continued to probe the life of the 29-year-old gunman for clues to what prompted the rampage that targeted diners at restaurants and cafes in a popular Toronto neighborhood.

The alleged assailant, Faisal Hussain, died after an exchange of gunfire with police. His family has said he suffered from lifelong “severe mental health challenges” but they never imagined he would do such a thing. It was not immediately clear whether he took his own life or was killed by police during the attack Sunday night.

On Tuesday, the Ministry of Public Safety knocked down suspicions of any links to terrorism.

“At this stage, based on the state of the investigation, which is led by the Toronto police service, there is no connection between that individual and national security,” Public Safety Minister Ralph Goodale said.

The mass shooting in Toronto’s Greektown neighborhood stunned people in a normally safe city, already unsettled by an attack just three months ago when a man used a van to plow over pedestrians on a downtown sidewalk, killing 10 people and injuring 14 in an attack apparently aimed at women.

Hussain’s family issued a statement saying their son had a long history of psychosis and depression and had not responded to numerous treatment approaches, including therapy and medication.

“While we did our best to seek help for him throughout his life of struggle and pain, we could never imagine that this would be his devastating and destructive end,” the family said. “Our hearts are in pieces for the victims and for our city as we all come to grips with this terrible tragedy. We will mourn those who were lost for the rest of our lives.”

Investigators searched the low-income apartment that Hussain shared with his parents and siblings on Thorncliffe Park Drive in the eastern part of the city, and removed boxes of potential evidence overnight. An autopsy on Hussain was expected Tuesday.

Where Hussain got his handgun remains unknown.

Canada overhauled its gun-control laws after the country’s worst mass shooting in 1989, when gunman Marc Lepine killed 14 women and himself at Montreal’s Ecole Polytechnique college. It is now illegal to possess an unregistered handgun or any kind of rapid-fire weapon. Canada also requires training, a personal risk assessment, two references, spousal notification and criminal record checks.

During a debate in City Council on Tuesday, Councilman Joe Cressy asked if Toronto could outright ban guns and was informed it would be up to the federal government to change the laws. Mayor John Tory has also questioned why anybody would need a gun in Toronto.

Don Peat, a spokesman for the mayor, said the Council was considering a motion urging the federal government to ban the sale of handguns and handgun ammunition in Toronto.

Canadians have long taken comfort in the peacefulness of their communities and are nervous about anything that might indicate they are moving closer to their American counterparts.

Still, though mass shootings are rare in Canada’s largest city, Toronto police had deployed dozens of additional officers over the weekend to deal with a recent rise in gun violence. The city has seen 23 gun homicides so far this year, compared to 16 fatal shootings in the first half of 2017.

Police Chief Mark Saunders said he would not speculate on the motive for Sunday’s attack.  “We do not know why this has happened yet,” he said. “It’s going to take some time.”

Among those killed, was 18-year-old Reese Fallon, a recent high school graduate who volunteered for Canada’s Liberal Party and was to attend McMaster University in the fall. Officials did not identify the other fatality, a 10-year-old girl, or name any of the 13 wounded, who included six women and girls, and seven men. The wounded ranged in age from 17 to 59.