ISIS has claimed responsibility for the mass shooting in Toronto that left two people dead — including a 10-year-old girl — and 13 injured.

The terror group routinely claims responsibility for acts of violence, and did not provide any evidence to support its claim.

The 10-year-old girl killed in the attack has been named as Julianna Kozis, from the Toronto suburb of Markham. The child was having dinner with her father at a cafe when she was gunned down by 29-year-old Faisal Hussain.

Trainee nurse Reese Fallon, 18, was also killed in the attack.

Canadian police are digging into the life of Hussain, seeking to explain what prompted him to fire a gun into restaurants and cafes in Toronto’s Greektown neighbourhood.

Earlier, the Ministry of Public Safety denied that Hussain had any link to terrorism.

media_camera A picture of Toronto gunman Faisal Hussain, supplied by a friend who took the image about two years ago.

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“At this time, there is no national-security nexus to the investigation,” said Hilary Peirce, a spokeswoman for Public Safety Minister Ralph Goodale.

Earlier, police identified the two victims who were killed in the shooting as ten-year-old Julianna Kozis and 18-year-old Reese Fallon.

media_camera This photo provided by the Toronto Police shows Julianna Kozis.

The family of Hussain, who died after an exchange of gunfire with police, said that he had long suffered from psychosis and depression 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 rampage on Sunday night, local time.

media_camera Friends of Toronto shooting victim Reese Fallon leave candles on pictures of the 18-year-old at a makeshift memorial. Picture: Mark Blinch/The Canadian Press via AP

The mass shooting in the Greektown district stunned people in a normally safe city that just three months ago saw a man use a van to plough over pedestrians on a footpath in another Toronto district, killing 10 people and injuring 14 in an attack apparently aimed at women.

A statement from Hussain’s relatives said he had lifelong “severe mental health challenges”. They said medication did not help him and the interventions of professionals were unsuccessful.

“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. They removed boxes of potential evidence overnight. An autopsy on Hussain was expected to take place on Tuesday.

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

media_camera The gunman was identified as Faisal Hussain. Picture: Instagram

Friends and family paid tribute to victim Reese Fallon, a recent high school graduate who volunteered for Canada’s Liberal Party and who was about to start university.

Her family said they were devastated. “She was … smart, passionate and full of energy. It is a huge loss,” said Nathaniel Erskine-Smith, a member of Parliament who knew Fallon. Flags at Toronto City Hall as well as at Fallon’s former high school were lowered to half-mast.

“An engaging student, Reese Fallon graduated from Malvern CI just last month and was highly regarded by staff and loved by her friends,” the school board said, adding that support was being offered to students.

media_camera Student Reese Fallon, 18, was killed by a gunman in Toronto. Picture: Facebook

Videos and witness accounts of the shootings showed Hussain dressed in black walking quickly down a footpath on Danforth Avenue, using a handgun to fire into shops and restaurants in the Greektown area, known for its of expensive homes, eateries and cafes.

media_camera Toronto has been hit hard by the shooting. Picture: Mark Blinch/The Canadian Press via AP

At the corner of Danforth Avenue and Logan Street, where some of the shots were fired, about 50 people milled about on a small square on Monday evening, talking in several languages. They expressed shock at a shooting in such a neighbourhood. Some hugged, some wept, and many said they wondered how the attacker obtained a gun in a country with far stricter gun laws than in the neighbouring US.

Police identify the Toronto shooter Police identify the Toronto shooter

People signed a makeshift memorial made of plywood reading: “We are Danforth strong.” “I’m out of my mind just thinking about it. It’s Toronto,” said Augustino Speciale, who paused to smell a bouquet of white lilies attached to a lamppost. Ontario’s police watchdog agency said there was an exchange of shots between the attacker and two policemen on a side street before the gunman was found dead.

media_camera A police forensic van sits parked in front of an apartment building where shooting suspect Faisal Hussain lived. Picture: AP

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.

Toronto has long prided itself as being one of the safest big cities in the world.

“We were so used to living in a city where these things didn’t happen and as we saw them going on in the world around us (we) thought they couldn’t happen here,” Mayor John Tory said. “This is an attack against innocent families and our entire city.”

media_camera Desirae Shapiro, 19, left, and her mother, Gina Shapiro, friends of shooting victim Reese Fallon, after visiting a makeshift memorial. Picture: Mark Blinch/The Canadian Press via AP

If you are experiencing mental health issues contact Lifeline on 13 11 14 or BeyondBlue 1300 224 636. If it is an emergency please call 000