Islamic state on Wednesday claimed responsibility for a shooting in Toronto on Sunday that killed two people and wounded 13, the group's propaganda arm said on Wednesday.

The attacker "was a soldier of the Islamic State and carried out the attack in response to calls to target the citizens of the coalition countries," a statement from AMAQ news agency said.

The group did not provide further detail or evidence for its claim. Canadian police have said the motive for the shooting remained unclear.

The assailant, Faisal Hussain, died after an exchange of gunfire with police. His family has said he suffered from lifelong "severe mental health challenges".

A statement issued by his family said their son had not responded to numerous treatment approaches, including therapy and medication, for long-term psychosis and depression