Nighisti Semret, 55, was attacked when walking home from work on Tuesday morning. Police say she was stabbed multiple times.
Police have since made contact with the slain woman’s family and notified them of her death.
Const. Tony Vella says investigators contacted the woman's mother, brothers and children in Uganda late Wednesday.
Police do not believe that Semret, a refugee from North Africa who worked as a cleaner at a downtown hotel, knew her attacker.
Vella says several witnesses have come forward, including a man who was able to confront an assailant brandishing a knife but was unable to stop him from fleeing.
By that time though, police say Semret had already suffered the fatal wounds.
On Thursday, several officers remained in the downtown neighbourhood where the mother of three was killed to canvass area residents.
Investigators also made a specific appeal Thursday for residents living in an area between Sherbourne and Ontario streets, north of Carlton Street and south of Wellesley Street, to scour their properties for "a discarded knife."
For residents and business owners in the same area, investigators are also asking that they review their surveillance tapes for anything suspicious that occurred between 6:30 a.m. and 7 a.m. on Tuesday.
Neighbourhood on edge
People living in Cabbagetown, the neighbourhood where Semret was killed, say they are feeling on edge.
Spiros Papathanasakis, the executive director of Cabbagetown Youth Centre, said there is a noticeable anxiety among residents going about their daily business.
"I walked out my door today … and a lady jumped walking her dog," he told CBC Radio's Metro Morning.
"So I guess she didn’t see me from the bushes and normally that same lady would be smiling and say: 'Good morning.'"
Former Toronto mayor Barbara Hall said she walks down the laneway where Semret was attacked on daily basis, as it’s the route she takes to work.
"People are shocked, they are very sad for the senseless, random loss of a life. But people are also feeling vulnerable," she told CBC News.
Karen McArthur has lived in Cabbagetown for 20 years and she says residents are banding together to make changes.
"This alleyway we determined needs to be lit via motion sensor, we’re thinking that we’ll just get right to it and get an electrician and get it in place," McArthur told CBC News on Thursday.
The laneway was lit up on Wednesday night for a vigil.
Another vigil will be held on Thursday evening, after which community members plan to march to Winchester Square Park to plant roses and a tree in honour of Semret.
Investigators have also posted surveillance video from a nearby apartment building on YouTube in hopes of identifying the suspect.
The video shows Semret being closely followed by the male suspect just prior to her death.
The suspect is described as a white male, about five-foot-10 to six-foot-two, 150 to 200 pounds, with a medium build. Police say he was wearing a dark coat, a light-coloured scarf and a dark hat.