Officials in Toronto are pushing for a ban on the sale of handguns and handgun ammunition, as Canada’s biggest city continues to reel from a shooting that left three people dead and injured 13 others.

“Why does anyone in this city need to have a gun at all?” John Tory, Toronto’s mayor, said on Tuesday as the city council passed a motion to urge the federal and provincial government to enact the ban.

Before Sunday’s shooting, councillors had already set aside the day to debate a range of initiatives aimed at tackling rising gun violence in the city – a discussion that took on new urgency after the attack.

Residents had been out enjoying a warm summer’s night when a lone gunman, later identified as Faisal Hussain, opened fire along one of the city’s liveliest stretches.

Two people were killed; recent high school graduate Reese Fallon, 18, and 10-year-old Julianna Kozis. Another 13 were injured in the attack.

Hussain, was found dead after he exchanged gunfire with police and fled, though it remains unclear whether he killed himself or was killed by police.

Police have yet to confirm how the gunman obtained a handgun, but the shooting has added impetus to calls for a ban on the sale of handguns and handgun ammunition in Toronto.

The ban would only apply within Toronto city limits, meaning that such purchases could still potentially be made in nearby cities. The ban would also probably do little to stem the flow of illegal guns into Canada from the US.

Still, about half of the illegal guns seized by police now come from domestic sources, such as those who buy guns legally and resell them, Toronto’s police chief, Mark Saunders, said on Tuesday.

Canada’s public safety minister said the ban was being considered but declined to offer a concrete timeline. “It is a complex proposition because it would entail a substantial rewriting of the criminal code,” Ralph Goodale told reporters.

Investigators are searching for answers about the gunman and his motive. Photograph: Canadian Press/Rex/Shutterstock

On Wednesday, as investigators continue to comb through the life of the 29-year-old gunman for clues that could explain the shooting, Isis claimed responsibility for the attack. The group’s propaganda agency did not offer any evidence, however, to support a statement that described the attacker as “one of the soldiers of the Islamic State”.

The assertion was swiftly shot down by Toronto’s police chief. “At this stage, we have no evidence to support these claims,” Saunders said in a statement.

His stance was echoed by Canada’s public safety minister, who said there was no connection between the gunman and any other national security issue.

Authorities have not yet speculated on a motive for the attack. In a statement, Hussain’s family cited his history of depression and psychosis, noting that professional help, medication and therapy had failed to help him.

“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,” they said.

Police have declined to say whether he was known to them.

Ontario’s ministry of the attorney general has said Hussain appears to have no criminal files associated with his name, though a spokesperson said the database used is not comprehensive. A source confirmed that Hussain did have prior contact with police, describing the interactions as mental health-related.