On Friday, police were called to a scene along a hiking trail near Jane Street and Alliance Avenue. That's where a woman's torso was found in the bag.
Since that discovery, police have searched a section of the Humber River control channel, as well as a number of dumpsters in the area.
On Tuesday morning, police held a news conference to update the media on their investigation.
Det. John Margetson told reporters that police believe the remains belong to a woman who came to Canada from Eritrea, though he cautioned that forensic testing will be necessary to confirm that suspicion.
"We suspect strongly who it is, but until a forensic confirmation is done and next of kin is notified, we can't release a name at this time," he said.
Police have arrested a suspect, 41-year-old Adonay Zekarias, who has been charged with committing an indignity to a dead body. He was due to appear in a Toronto court on Tuesday.
It is not yet clear how or why the woman died.
Margetson said the suspect and the presumed victim were "known to each other," though the detective did not provide much detail on the extent of their relationship.
"They've been acquaintances and they are from the same country," he said.
Police have obtained a search warrant for a residence at 101 Humber Blvd., where the suspect lives, Margetson said.
Investigators have also been searching a 15th floor apartment at 285 Shuter St., where police believe the victim lived.
"We are looking for a substantial amount of human remains still missing," Margetson said.Suggest a correction