Teenager Reese Fallon has been identified as one of the two victims of a shooting that left 13 others injured as Canadian authorities name the man they believe was behind yesterday's attack.

Ms Fallon, 18, and a 10-year-old girl were killed in the shooting spree in Toronto's Greektown district after Faisal Hussain, 29, opened fire.

The 29-year-old walked along a Toronto street firing a handgun into restaurants and cafes, shooting his victims before being killed in an exchange of gunfire with police.

In a statement, Hussain's family expressed their devastation over the tragedy and said he had long struggled with severe mental illness.

"We are utterly devastated by the incomprehensible news that our son was responsible for the senseless violence and loss of life," they said, 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."

Ms Fallon was a volunteer for Canada's Liberal party, with a statement from her family saying her loss had been devastating.

"She was ... smart, passionate and full of energy. It is a huge loss," said Canadian MP Nathaniel Erskine-Smith, who knew Ms Fallon.

An online Facebook profile said she was a student of McMaster University.

Police Chief Mark Saunders said the shooting on Sunday night in the city's bustling Greektown neighbourhood was not random and he did not rule out terrorism as a motive.

Mr Saunders said authorities "do not know why this has happened yet."

The other victims range from 10-years-old to 59 and their injuries range from minor to serious.

"It's almost inconceivable that these things can happen," said Mayor John Tory. "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."

"This is an attack against innocent families and our entire city."

A video from one witness shows a man dressed in black clothes and a black hat walking quickly and firing three shots from the footpath into at least one shop or restaurant.

Police located the suspect about three blocks away from the scene and exchanged fire. He was found dead back on Danforth Street after fleeing.

Witnesses heard many shots and described the suspect walking past restaurants and cafes and patios on both sides of the street and firing into them.

John Tulloch said he and his brother had just gotten out of their car when he heard about 20 to 30 gunshots.

"We just ran. We saw people starting to run so we just ran," he said.

An army of police, paramedics and other first responders quickly descended on the scene, while area residents, some in their pyjamas, emerged from their homes to see what was happening.

Toronto Councillor Paula Fletcher told CP24 she heard that the gunman was emotionally disturbed.

"It's not gang related. It looks like someone who is very disturbed," Fletcher said.

Mr Fletcher said for this to happen in an area where families gather for dinner is a tragedy.

This past weekend Toronto police deployed dozens of additional officers to deal with a recent spike in gun violence in the city. Mr Tory said the city has a gun problem.

"Guns are too readily available to too many people," Mr Tory said.

Australia's Department of Foreign Affairs and Trade said the high commission in Ottawa had been advised by local authorities that "no Australians are known to be among those injured in the shooting in the Greektown area of Toronto."

The mass shooting comes a few months after a driver of a van ploughed into pedestrians on a Toronto sidewalk, killing 10 people and injuring 14.

Authorities have not disclosed a motive but have said the arrested driver, Alek Minassian, posted a message on social media referencing a misogynistic online community before the attack.