ISIS claimed responsibility Wednesday for the deadly Toronto shooting and investigators are reportedly digging into the gunman's past and Internet history -- but Canadian officials continue to insist the killings aren't related to terrorism, clouding the possible motive for the attack that killed two and wounded 13.

The terror group's AMAQ propaganda agency, citing a "security source," said Toronto shooter Faisal Hussain, 29, was a "soldier of the Islamic State and carried out the attack in response to calls to target the citizens of the coalition countries." Based on language used in previous claims by ISIS, it appeared the shrinking Islamist group looked at Hussain as having been merely inspired by ISIS, rather than having been directed.

The group did not provide further details or any evidence, such as a videotaped pledge of allegiance, for its claim. Hussain, who killed 10-year-old Julianna Kozis and 18-year-old Reese Fallon during the mass shooting, died after a gun battle with police late Sunday.

An undated photo of Faisal Hussain, the Toronto shooter. (Courtesy of The family of Faisal Hussain via AP)

On Wednesday, Canadian officials stressed there was no national security risk despite authorities' continued investigation into what prompted the deadly rampage in the bustling Greektown neighborhood.

"These are the early stages‎ of an active investigation being led by the Toronto Police Service," a spokesperson from Canada's Office of the Minister of Public Safety and Emergency Preparedness told Fox News. "At this time, there is no national security nexus."

But while officials are publicly pushing back on any ties to terror for now, reports have emerged that investigators are questioning Hussain's past.

People add flowers and messages to a memorial for the victims of Sunday's shooting in Toronto. (Mark Blinch/The Canadian Press via AP)

Hussain had visited ISIS websites and may have expressed support for the terrorist group, CBS News and the Toronto Sun reported, citing law enforcement sources. A law enforcement source told the Toronto Sun the 29-year-old expressed “support” for a website that was seen as “pro" ISIS.

Officials are also investigating if Hussain lived at one time in Afghanistan or possibly Pakistan, CBS News reported.

Hussain's online activities have previously drawn the attention of law enforcement, and he was “well known to Toronto Police” for investigations into past crimes “involving weapons and violence," according to the Toronto Sun.

TORONTO MASS SHOOTING SUSPECT WAS KNOWN TO POLICE DUE TO MENTAL HEALTH ISSUES, REPORT SAYS

Toronto Police Chief Mark Saunders pushed back on those reports on Wednesday, saying there is so far no evidence of ISIS support and that that "every investigative avenue" is being examined.

Police are shown at the perimeter of the scene of the shooting in east Toronto. (Christopher Katsarov/The Canadian Press via AP)

“Since Sunday evening, all areas of the Toronto Police Service have been involved in this investigation. We have received assistance from law enforcement partners at every level and I have been updated regularly. At this stage, we have no evidence to support these claims," Saunders said in a statement. "Accurate information about this investigation will only be released by the Toronto Police Service. 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.”

The gunman's family has maintained their son had a long history of psychosis and depression and had not responded to numerous treatment approaches, including therapy and medication.

"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 family said in a statement. "Our hearts are in pieces for the victims and for our city as we all come to grips with this terrible tragedy. We will mourn those who were lost for the rest of our lives."

Julianna Kozis, 10, was killed in the shooting rampage on Sunday in Toronto's popular Greektown neighborhood. (Family of Julianna Kozis/Toronto Police via AP)

Canada's Global News reported Tuesday that Hussain had been taken into police custody twice due to concerns about his mental health. The Global News report did not specify when Toronto police had encountered Hussain, but said he had a history of mental health concerns dating back to 2010. The report also did not say what happened after police apprehended Hussain.

TORONTO SHOOTING SUSPECT IDENTIFIED AS FAISAL HUSSAIN, FAMILY SAYS HE HAD 'SEVERE MENTAL HEALTH CHALLENGES'

A police source told Global News that Hussain believed he was the Joker character from the "Batman" movies. The source added Hussain "was fascinated with death and explosions. He also liked replica handguns." A family spokesman confirmed to Global News that Hussain owned a replica BB gun, but denied he had any special obsession with the Batman movies or any particular character.

Investigators searched the low-income apartment Hussain shared with his parents and siblings on Thorncliffe Park Drive in the eastern part of the city, and removed boxes filled with potential evidence overnight, according to the Associated Press.

People hold signs at a memorial remembering the victims of Sunday's shooting in Toronto. (Mark Blinch/The Canadian Press via AP)

An autopsy on Hussain was expected Tuesday, and officials have not yet disclosed where Hussain got the handgun used in the attack.

Fox News' Catherine Herridge, Samuel Chamberlain and The Associated Press contributed to this report.