The family of the man accused of killing two people and wounding more than a dozen others in a Toronto shooting spree say he struggled with severe mental illness as police continue to seek a motive.

Less than a day after a 10-year-old girl and an 18-year-old woman died in the shooting and 13 others were wounded, police identified the suspect as 29-year-old Toronto resident Faisal Hussain. He was found dead shortly after the shooting, authorities say.

“We do not know why this happened,” Toronto Police Chief Mark Saunders told reporters on Monday, adding that he would not speculate about the gunman’s motive.

“It’s way too early to rule out anything.”

The suspect, armed with a handgun, opened fire at 10pm (local time) on Sunday on a stretch of Danforth Avenue filled with restaurants and family-friendly attractions in the city’s Greektown neighbourhood, Canada’s Special Investigations Unit (SIU) said.

Chilling footage published by the Canadian Broadcasting Corporation on Tuesday showed Hussain as he went on his random shooting spree.

The video, first posted on social media by a witness to the shootings, shows the gunman as he casually stalked the busy street before taking aim on a pedestrian.

Warning. Shooting video below:

Hussain’s family issued a statement expressing their shock at his alleged actions.

“We are utterly devastated by the incomprehensible news that our son was responsible for the senseless violence and loss of life,” the family wrote in a statement, adding that he suffered from severe mental illness as well as from “psychosis and depression his entire life.”

“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 statement said.

While police are yet to formally identify the two people killed in the attack, local politician Nathaniel Erskine-Smith confirmed the 18-year-old victim was Reese Fallon, a recent high school graduate who planned to study nursing. 

Reece Fallon, 18, was due to attend McMaster University to study nursing. Photo: AAP

“The family is devastated,” Mr Erskine-Smith said, adding that they have asked for privacy while they mourn a young woman who was “smart, passionate and full of energy”.

The gunman exchanged fire with police, fled and was later found dead, according to the SIU, which investigates deaths and injuries involving police.

The suspect had a gunshot wound, authorities said, but would not elaborate on the circumstances or cause of his death. An autopsy will be conducted on Tuesday, SIU spokeswoman Monica Hudon said.

Hours after the fatal shooting, in an apparently unrelated incident, a man with a knife was arrested during a military ceremony on Parliament Hill in Canada’s capital, Ottawa. The Defense Ministry said no one was injured and gave no further details.

Prime Minister Justin Trudeau wrote on Twitter on Monday: “The people of Toronto are strong, resilient and brave – and we’ll be there to support you through this difficult time.”

My thoughts are with everyone affected by the terrible tragedy on the Danforth last night in Toronto, and may the injured make a full recovery. The people of Toronto are strong, resilient and brave – and we’ll be there to support you through this difficult time.

— Justin Trudeau (@JustinTrudeau) July 23, 2018

Toronto Mayor John Tory told reporters the city has a gun problem, with weapons too readily available to too many people.

“Why does anyone in this city need to have a gun at all?” he asked in an address to city councillors early on Monday.

Canada’s crime rate rose by one per cent in 2017, the third consecutive annual increase, according to Statistics Canada.

The murder rate jumped by seven per cent, due largely to killings in British Columbia and Quebec, while crime involving guns grew by seven per cent.

Toronto is grappling with a sharp rise in gun violence as gun deaths jumped to 26, up 53 per cent so far this year from the same period in 2017. The number of shootings has risen 13 per cent.

In April, a driver deliberately ploughed a rental van into a lunch-hour crowd in Toronto, police said, killing 10 people and injuring 15 along a 1.6km stretch of footpath thronged with pedestrians.

-with AAP