Police say Rigat Ghirmay, 28, of Toronto, was last seen alive on May 15 and are asking for the public's help in tracing her movements in the final days of her life.
The bag containing Ghirmay's remains was found May 24, but Det. John Margetson said Monday that only about one-third of her body has been recovered.
"We've been unable to locate the rest of her body," Margetson said at a news conference.
"Whether or not it went into the garbage, went into the river (or is) spread throughout the area, we're not sure."
Investigators are looking to speak with anyone who saw a person walking in that area with a black, yellow and green duffel bag with rollers, some time in the past two weeks.
Margetson said it's believed Ghirmay knew the man accused in her case, but that police have yet to figure out just what their connection was.
"There's some conflicting information as to what type of relationship they had," he said.
"We know that they were known to each other and they frequented places together, and at one time lived together as well," Margetson said, adding the evidence indicates the accused acted alone.
Anyone who knew Ghirmay or the Toronto man charged in the case is asked to contact police.
Adonay Zekarias, 41, has been charged with causing an indignity to a dead body, but Margetson said there is a "high likelihood" the charges will be upgraded to murder.
The coroner has not yet determined the cause of death and Margetson said it may take some time to do so.
Last week, police said they were searching garbage at transfer stations but that no remains were found there.
Police say Ghirmay came from the African country of Eritrea but had lived in Canada for a while. Zekarias is also from Eritrea.