Toronto Police Chief Mark Saunders said yesterday officials have found no evidence to support the Islamic State group's claim of responsibility for Sunday's mass shooting in Toronto that killed two and injured 13.

The Islamic State claimed that one of its "soldiers" carried out the attack in response to its calls to target citizens of the US-led coalition battling it. The claim appears on one of the group's social media channels, and a security member of Isis was quoted speaking to the group's Amaq news agency.

Saunders said in a statement that all areas of the Toronto Police Service have been involved in the investigation and they have received assistance from law enforcement partners at every level.

This undated photo provided by the Toronto Police shows Julianna Kozis, 10, who was killed in the Toronto shooting. Photo / via AP
This undated photo provided by the Toronto Police shows Julianna Kozis, 10, who was killed in the Toronto shooting. Photo / via AP

"At this stage, we have no evidence to support these claims," Saunders said.

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Saunders said officials will continue to explore every investigative avenue, including interviews and reviewing the online activity and mental health experiences of dead gunman Faisal Hussain.

Federal Public Safety Minister Ralph Goodale has also said there was no national security risk following the attack.

Hussain died after an exchange of gunfire with police. His family has said he suffered from lifelong "severe mental health challenges" including psychosis and depression and had not responded to numerous treatment approaches, including therapy and medication.

Late Tuesday, authorities identified the 10-year-old girl who was slain as Julianna Kozis of Markham, Ontario. Toronto police released a photo of the smiling, young girl and said her family had asked for privacy during their time of grief. Police previously identified the other person killed in the shooting as 18-year-old Reese Fallon of Toronto

Kozis was involved in synchronised swimming, and her Markham Synchro Club issued a statement calling her "a beautiful, aspiring athlete."

The city of Markham paid tribute to Kozis by lowering flags and opening a book of condolence. The girl's photo and a memory book sat on a table inside Markham city hall, surrounded by delicate pink rose petals.

A photograph of Julianna Kozis is seen at a memorial assembled by the city of Markham, at the Markham Civic Centre. Photo / AP
A photograph of Julianna Kozis is seen at a memorial assembled by the city of Markham, at the Markham Civic Centre. Photo / AP

"Right now we need to focus on respecting the family's wishes for privacy as they deal with a horrible loss," Mayor Frank Scarpitti said yesterday.  "When we heard it was a 10-year-old girl from Markham, all of our hearts dropped."

The mass shooting in Toronto's Greektown neighbourhood stunned people in a normally safe city, already unsettled by an attack just three months ago when a man used a van to plow over pedestrians on a downtown sidewalk, killing 10 people and injuring 14 in an attack apparently aimed at women.

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Toronto Mayor John Tory and some city councilors had lunch Wednesday at a Greek restaurant on the street where the shooting occurred.

"We're here to show support," Tory said, adding he planned to attend a candlelight vigil in the evening.

- AP