One of the hands was discovered in the Credit River — in the same area where the foot was found on Wednesday — while the other hand was a "considerable distance" downstream, said Sgt. Pete Brandwood of Peel Regional Police, the force responsible for the area that includes Mississauga.
It's not clear if the left and right hands are from the same person as the severed foot and head, but it seems safe to assume so, Brandwood said.
"The likelihood of it being the same person, common-sense wise, is probably pretty high," Brandwood told a news conference on Friday afternoon.
He said investigators are examining an additional discovery, but police said later that the coroner had determined it was animal remains.
Brandwood said he is optimistic more evidence will emerge as roughly 50 police officers and other searchers scour the water, parklands and surrounding rocky hills.
"We're working on the assumption that if you find one thing, and you keep finding more, eventually you're going to find everything," Brandwood said.
And Brandwood said there is no indication the gruesome discoveries are the work of a copycat killer in the shadow of Luka Rocco Magnotta, who is accused of the murder and dismemberment of a Montreal student.
"There is nothing to suggest... that there is any link to Luka Magnotta," Brandwood said.
Const. George Tudos said the search will continue through the weekend.
"We're just hoping that the weather plays a role here to assist us and that we can complete this investigation and have some answers," he said, noting that identifying the body is a priority.
Authorities discovered a woman's head Thursday in the river where it runs through Hewick Meadows Park a day after hikers came across a woman's severed foot.
Police can't say if the body parts were placed where they were found or if they drifted there from another point upstream in the river, which flows from headwaters above the Niagara Escarpment to Lake Ontario.
The pastor of a church not far from where the body parts were discovered said he was surprised to hear of the string of grim discoveries, but is not worried for the safety of the community.
"We're deeply shocked and saddened by the discovery. We're praying that the police will be able to get to the bottom of this and help determine whether this was a criminal activity in the neighbourhood (or) was it something that happened in another region," said Doug Rhind of the Portico community church.