A police officer stands guard at the scene of a mass shooting in Toronto, Canada (Reuters)

The ISIS on Wednesday claimed responsibility for a weekend shooting that killed two people in Canada's Toronto.

The group's propaganda agency Amaq said the attacker was "one of the soldiers of the Islamic State".

"He carried out the attack in response to calls to target nationals of countries of the coalition" fighting ISIS in Syria and Iraq since 2014, it said.

Faisal Hussain, 29, killed a 18-year-old woman and a 10-year-old girl in the shooting rampage on a Toronto street on Sunday evening, Canadian police said.

He was found dead near the scene of the shooting after an exchange of gunfire with police.

The attack in Toronto's bustling Greektown neighbourhood at around 10:00 pm Sunday also wounded 13 people aged 10 to 59, officials said.

Hussain's family, in a statement to CBC News, denounced his "horrific actions" and said he was suffering from mental problems.

The said he had battled "severe mental health challenges, struggling with psychosis and depression his entire life".

They said medications and therapy had been unable to treat him.

Video footage posted by Canadian media showed Hussain, clad all in black, walking on a sidewalk and suddenly pulling out a handgun and shooting into a restaurant.

Witnesses said the shooting rampage lasted just a few minutes and sparked panic in the district, popular for its bars and restaurants.

Andrew Mantzios told The Globe and Mail newspaper he had seen the shooting as he sat with friends drinking coffee.

He said "a lady tried to run and she fell down", after which the shooter "turned around and shot her point blank, two or three times".

Toronto Mayor John Tory called the shooting "evidence of a gun problem" in the city.

ISIS overran large parts of Syria and neighbouring Iraq in 2014, but have since been ousted from most of that territory.

The terrorist group has claimed a string of deadly attacks in the West in recent years.

Canadian citizens have also been intercepted trying to reach Syria to join ISIS.