TORONTO police have identified the gunman who killed two people and wounded 13 others before he was killed during a shootout with police.

He was 29-year-old Faisal Hussain, of Toronto.

His family has issued a statement describing their grief and shock at his action: “We are at a terrible loss for words but we must speak out to express our deepest condolences to the families who are now suffering on account of our son’s horrific actions”.

“We are utterly devastated by the incomprehensible news that our son was responsible for the senseless violence and loss of life that took place on the Danfroth.

“Our son had severe mental health challenges, struggling with psychosis and depression his entire life … 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.

“Our hearts are in pieces for the victims and for our city as we all come to grips with this terrible tragedy”.

The Ontario Special Investigations Unit determined the gunman’s identity during investigations after the shooting.

A press release issued by the SIU said the decision to release the name was made after speaking to his family, and “due to the exceptional circumstances of this tragic incident and the public interest in knowing the man’s identity”.

The unit is reportedly executing a search warrant at the Thorncliffe Park suburb apartment where Faisal lived with his family.

Toronto Police Chief Mark Saunders said he was still investigating the motive behind the attack.

“I’m keeping everything open. Looking at every single possible motive for this; when you have this many people struck by gunfire, it’s a grave concern,” he said.

“I certainly want to find out exactly what it is, so I am not closing any doors or any chapters on this. I certainly don’t want to speculate… I don’t know why he did what he did, and he won’t be able to tell us because he is deceased.”

He did not rule out whether terrorism or gang violence was a factor.

He has also appealed for more witnesses to come forward to help build a complete narrative of the events surrounding yesterday’s shooting at the popular restaurant and nightclub strip.

“We do not know why this happened yet,” Chief Saunders told a news conference. “The investigation itself is very fluid, it is very new, it’s going to take some time.”

Toronto’s police chief says a 10 year-old girl and an 18-year-old woman were killed in the mass shooting in the city’s Greektown neighbourhood.

Police chief Mark Saunders said 13 other victims have injuries ranging from minor to serious. They range in age from 10 to 59.

One of the victims was Reese Fallon, 18, who was celebrating a birthday with two friends when she was killed.

Reese had graduated high school and was going to study nursing when she was killed by Hussain who began his shooting ramapge on the popular restaurant strip at about 10pm local time (12.30pm AEST) yesterday.

Her local MP, Nathaniel Erskine-Smith, identified her as one of two people killed.

Erskine-Smith told CityNews that Reese’s family “hasn’t processed this yet”.

“They’re devastated, as any parent would be,” he said.

A woman, who identified herself as Reese’s cousin, said she was “heartbroken”.

“My beautiful cousin. My heart hurts seeing this everywhere,” she wrote in a tribute.

“Seeing my friends mark themselves as safe on Facebook. But Reese can’t mark herself safe. I’m so devastated for her and her family. I’m in f***ing shock.”

Two of the injured victims in hospital are believed to be Reese’s friends.

A vigil is being held on Monday for the victims at a church on Danforth.

Noon A hospital says five of the 14 people shot by a gunman who went on a deadly rampage on a Toronto street are in serious or critical, but stable, condition.

St. Michael’s Hospital trauma surgeon Dr. Najma Ahmed says three of those people underwent immediate operations to save their lives.

The 29-year-old gunman was killed after an exchange of gunfire with police. It was not immediately clear whether the man killed himself or died of injuries after being shot by police.

The Special Investigations Unit will determine how the Hussain died and whether there was any police wrongdoing. The unit is automatically called in to investigate all deaths and serious injuries where police are involved.