The agency that investigates police-involved shootings said Monday morning the suspect was a 29-year-old man who had fired shots at groups of people several times while walking along Danforth Avenue.
Police investigate a vehicle at the scene of a shooting in Toronto, Monday (local time).
He died after an exchange of gunfire with police on Sunday night.
Hussain killed a 10-year-old girl and an 18-year-old woman and wounded 13 other people, some seriously.
Motives for the attack have not been discerned, and the gunman has yet to be identified by police.
Bill Blair, the former Toronto City Police chief who was appointed last week as minister responsible for reducing organized crime, said lawmakers should be looking at more than simply handguns as they work to get illegal weapons off the streets.
Hussain's family released a statement Tuesday, saying they were "utterly devastated" by the attack.
Hussain's family said he had suffered since infancy from serious mental problems, which treatment and medication were unable to overcome.
The relatives say their "hearts are in pieces for the victims".
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Deaths from gun violence in the city jumped by 53 percent to 26 so far in 2018 from the same period past year, police data last week showed, with the number of shootings rising by 13 percent. "We still live in a great city", he said, "but we have to be ever more vigilant about this kind of things". Residents of the neighborhood said Hussain's family has suffered other tragedies in recent years, including the death of Hussain's sister from a vehicle crash.
The 29-year-old brutally gunned down his victims, who included aspiring nurse Reese Fallon, 18, and a 10-year-old girl.
Anthony Parise, who taught Fallon's Grade 12 English class, remembered her as "a leader among her peers" who planned to become a nurse.
He died after an exchange of gunfire with police but investigators have yet to say whether he took his own life or was killed by police. She was always so kind, " said Frank Hong.
"I promise all of the people of Toronto, but most importantly those directly affected by this tragedy, that we will all be relentless in getting answers about why this senseless attack happened", Tory said.
"I'm out of my mind just thinking about it".
"It's they, the federal government, who has to consider it, together with what I proposed yesterday, which was the toughening of existing laws on things like gun trafficking, and making it a little more hard for people who have had mental issues or domestic violence involvement to get a gun permit", he said.
With more than 2 million people, Toronto is among the biggest cities in North America.
"We just ran", he said. "This is an attack against innocent families and our entire city".
In April, the driver of a van plowed into pedestrians on a Toronto sidewalk, killing 10 people and injuring 14.