Police began their search after some body parts were found in a duffel bag along a trail on the west side of the city, the Toronto Star reported Tuesday.
The name of the victim has not been released, although authorities say in court documents she is Rigat Ghirmay, whom they identify as the girlfriend of Adonay Zekarias.
Zekarias, 41, who also is believed to be from Eritrea, was arrested Sunday after the remains were found Friday. He has been charged with indignity to a dead body.
Police detective John Margetson said the remains in the bag appeared to have died in the last two weeks.
Tuesday, police searched Ghirmay's apartment in downtown Toronto as well Zekarias' home and eight dumpsters in his neighborhood.
Elen Haile, who formerly worked with Zekarias and Ghirmay, said the pair worked together in 2011 as cleaning staff at a Toronto hotel.
Haile didn't know if the two had dated, but said they were very close friends and "whatever place they go, they go together."
Zekarias is being detained without bond until an interpreter can be located for a hearing.
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