Toronto police are desperately searching for the motive for a seemingly random shooting rampage that left three people dead, including the gunman, and 13 others wounded.

A 10-year-old girl died overnight, becoming the second victim of the shooting on a busy restaurant-filled street that had already claimed the lives of an 18-year-old woman and the 29-year-old attacker.

“We do not know why this happened,” Toronto Police Chief Mark Saunders said on Tuesday morning (AEST), adding that he would not speculate about the gunman’s motive.

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

The suspect, Toronto resident Faisal Hussain, opened fire with a handgun at 10pm local time on Sunday on a stretch of Danforth Avenue filled with family-friendly attractions in the city’s Greektown neighbourhood, police, said.

Witnesses reported that the gunman walked down the busy avenue firing apparently at random.

The identities of the two female victims have not been released and no Australians are known to be among the injured.

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

Hussain had a gunshot wound, but authorities would not elaborate on the circumstances or cause of his death.

Chief Saunders said 13 people were sent to hospital with “minor to life-changing injuries”.

In a statement Tuesday morning, Hussain’s family said he “had severe mental health challenges, struggling with psychosis and depression his entire life”.

One witness, Carrie Lahey, told Canadian boradcaster CBC she was having dinner at a restaurant in when she saw a woman get shot right in front of her.

Ms Lahey was at the 7Numbers restaurant when the gunman entered.

“We were sitting out on the patio and we heard shots … so we went inside … and then he came in the restaurant and he shot the girl right in front of me,” she said.

“It went right through her lungs … thank God for the cops, because the paramedics showed up so late that the cops saved her life.”

Chief Saunders urged the public to share any information they have about the shooting, including video, saying police are “looking at every single possible motive for this”.

Canadian Prime Minister Justin Trudeau promised support for the victims.

“The people of Toronto are strong, resilient and brave – and we’ll be there to support you through this difficult time,” Mr Trudeau said in a Twitter post Monday.

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 Monday morning.

To own a gun in Canada an individual must apply for a licence, pass a background check and pass a firearm safety test.

Guns must be kept locked and unloaded and can only be legally carried outside the home with a special permit. Handguns and other restricted firearms require passing an additional course.

Canada’s crime rate rose by 1 per cent in 2017, the third consecutive annual increase, according to Statistics Canada.

The murder rate jumped by 7 per cent, due largely to killings in British Columbia and Quebec, while crime involving guns grew by 7 per cent.

Toronto is grappling with a sharp rise in gun violence this year.

Deaths from gun violence has jumped 53 per cent to 26 so far this year from the same period last year, police data last week showed, with the number of shootings rising 13 per cent.

-with AAP