There was an exchange of gunfire between police and the suspect, who was armed with a handgun, authorities said.
ISIS had claimed credit for the Sunday night attack which killed an 18-year-old woman and a 10-year-old girl.
She described the family matriarch as very kind and caring, but said the family troubles showed. "Medications and therapy were unable to treat him", they said.
"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.
According to videos and witness accounts, the assailant, clad all in black, was seen walking quickly down a sidewalk on Danforth Avenue, firing a handgun into shops and restaurants in Greektown, a district of expensive homes, eateries and cafes.
Toronto police have been seeking videos and photos from people nearby.
No officers were injured during the incident.
Newstalk1010 reports that the father of the 10-year-old victim was also wounded in the shooting and was brought from St. Michael's Hospital, where he is being treated, to his daughter's bedside at Sick Kids to say goodbye.
Police Chief Mark Saunders said an 18-year-old woman and a 10-year-old girl were killed in the shooting.
She and a several dozen of her classmates in a government relations class at York University attended the City Council session on Tuesday where council members discussed gun violence with the city's police chief. "Absolutely everything is open right now". They expressed shock at a shooting in such a neighborhood.
Sgt. Terry Brown said that some of those injured have light injuries, but some have "life-altering" injuries.
Andrew Mantzios told The Globe and Mail newspaper he had seen the shooting as he sat with friends drinking coffee.
Authorities have been responding to an uptick in violence, including an incident in May when two people set off a bomb inside an Indian restaurant in the Toronto suburb of Mississauga.
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"And then a lady tried to run and she fell down", he said. "He turned around and shot her point blank, two or three times".
Toronto is grappling with a sharp rise in gun violence this year. "Gun violence in any part of our city is disgusting and completely unacceptable".
"And then, I saw the carnage as I ran down the street here to kind of follow the gunfire", the man told CTV, who described the scene as "pretty insane".
"He was running across the street yelling something and then he fired six to 10 shots into the Second Cup", said Balkos.
'There must've been 20, 30 shots, altogether. It was a lot.
Jody Steinhauer told CBC News she was at a neighborhood restaurant with her family when she heard what sounded like 10 to 15 blasts of firecrackers.
She said the gunman's mother had told her about the relatively recent death of her daughter and an unspecified illness affecting her other son.
"We started to hear people scream out front", Steinhauer told the broadcaster.
The mayor later issued a statement saying he'd talked to Ontario Premier Doug Ford who conveyed his condolences on behalf of the province and offered any assistance required.
You shouldn't be punishing the rest of Canada because Toronto can't fix its problem, Cox said.
Choking back tears, Toronto Councillor Mary Fragedakis said to the city council Monday morning, "This is so heartbreaking". "And that leads to another question we need to discuss: Why does anyone in this city need to have a gun at all?"
On Monday evening, Toronto police were executing a search warrant at an apartment in a densely populated neighbourhood in east Toronto, where the suspect lived. That includes having 200 extra officers on shifts in specific neighbourhoods between the hours of 7 pm and 3 am - when most shootings occur.