The Toronto police chief says that there is no evidence that the Islamic State terror group is behind a mass shooting attack in the city this week, despite claims by the group.

Two people were killed and 14 others wounded when 29-year-old Faisal Hussain opened fire into restaurants in a busy neighborhood.

The terror group claimed that Hussain, who was killed after exchanging fire with officers, carried out the attack as a response to calls to target citizens of coalition countries.

Investigators had said that Hussain visited Islamic State websites and may have supported the terrorist group.

But Toronto Police Chief Mark Saunders said Wednesday in a statement "At this stage, we have no evidence to support these claims."

Public Safety Minister Ralph Goodale said that there is no risk to national security following the attack.

"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," Goodale said.

Toronto police identified the two victims as 10-year-old Julianna Kozis and 18-year-old Reese Fallon.

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."

It was not immediately known where Hussain obtained his firearm.

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 and said he supported a motion urging the federal government to ban the sale of handguns in Toronto. It passed on a 41-4 vote.

"People in the city of Toronto don't need handguns," Tory said.

Goodale earlier said Ottawa was already considering tightening handgun laws even before Sunday's shooting.