MONTREAL - Canadian authorities said Wednesday they have no evidence to substantiate a claim by the Islamic State group that the gunman who killed two people in a Toronto rampage was an IS fighter.

The group’s Amaq news agency said the gunman, identified by police as 29-year-old Faisal Hussain, was an IS “soldier” responding to its calls for attacks on nationals from countries fighting the group in Iraq and Syria. “At this stage, we have no evidence to support these claims,” Toronto police said in a statement.

“We will continue to explore every investigative avenue, including interviewing those who knew Mr Hussain, reviewing his online activity, and looking into his experiences with mental health,” police spokeswoman Meaghan Gray said.

The attack occurred Sunday night in Toronto’s Greektown area when the shooter opened fire at people on a crowded street before turning his attention to nearby restaurants.

Rushing to the scene, police exchanged fire with the gunman, who was found dead in an alleyway.

An 18-year-old woman and a 10-year-old girl were killed in the rampage, and 13 people were wounded.

Hussain’s family said he had suffered since infancy from serious mental problems, which treatment and medication were unable to overcome.

In a statement, the family said Hussain had battled “severe mental health challenges, struggling with psychosis and depression his entire life.”

On Wednesday, however, Amaq claimed that Hussain “carried out the attack in response to calls to target nationals of countries of the coalition” that has been fighting IS in Syria and Iraq since 2014.

A day earlier, Canada’s Minister of Public Safety Ralph Goodale had said: “There is no national security connection between this individual and any other national security issue.”

Hussain had no prior criminal record and had not been on the radar of Canada’s security agencies, he said.

The Toronto Star reported Wednesday that Hussain worked at the same Loblaws supermarket chain as two of the shooting victims - Reese Fallon, the 18-year-old killed in the attack, and Samantha Price, who was wounded. Loblaws called it a “tragic coincidence.”

It was the third time that Islamic State has claimed an attack in Canada, according to Amarnath Amarasingam, a Canadian researcher at the London-based Institute for Strategic Dialogue.

The first was in 2014 when it said two attacks against Canadian soldiers, one south of Montreal and the other in Ottawa, were “the direct result” of its call a month earlier for attacks on the West.

In 2016, it again claimed responsibility when a Canadian national, surrounded by police, detonated a bomb in a taxi in southern Ontario before being shot to death by police.

Amarasingam said he was “very skeptical” about the latest IS claim.