The body parts arrived about an hour apart at two schools, a waterfront public school near Vancouver's popular Granville Island and a posh private boys school in the city's west side.
Police suggested those two destinations may have been random.
"There's no indication that any students and staff have been targeted at either school," Deputy Chief Warren Lemcke of the Vancouver police told reporters at a late afternoon news conference.
"This must have been a very, very traumatic incident for all involved at the schools that were involved in opening these packages."
The discoveries came several days after two similar packages were mailed to Ottawa containing another hand and foot. Police have said those body parts belonged to Chinese student Jun Lin, whose torso was found in a back alley in Montreal with the hands, feet and head removed.
Lin's death prompted an international manhunt for Magnotta, who was arrested in Berlin on Monday and is expected to be extradited to Canada.
In Vancouver, police said a human hand arrived at False Creek Elementary School around 1 p.m. About an hour later, a foot arrived at St. George's, the private boys school.
Lemcke had few details to offer, but said Vancouver investigators were talking to their counterparts in Montreal.
"The investigation is only a few hours old now, so I can't link it to anything right now," said Lemcke.
"We have liased with Montreal and we'll liase with any other police agencies that we need to in the course of the investigation."
Lemcke said the B.C. Coroners Service was helping to identify the remains. Investigators were also working to determine where the packages were sent from, he said.
He couldn't say whether the packages were delivered through Canada Post or by a courier.
At St. George's, Grade 7 student Devon Mussio said his mother told him the news.
"I thought she was lying and I was like, 'Whoa, that's disturbing,'" said Mussio, who was standing outside the school with his mother, Penny.
"This guy's, like, a creep."
Both schools were expected to be open for classes on Wednesday, and each said counsellors would be on hand if any students needed help dealing with the news.
Barb Schoeber, whose two sons attend False Creek Elementary, said she didn't know what to tell her children and worried they would hear about it from older students.
"I may wait for them to hear it and see what kinds of questions come up and approach it that way," said Schoeber, whose boys are in Grades 1 and 3.
"I really don't know how I'm going to explain it to them, I really don't."
Schoeber said her thoughts were with the staff members who opened the packages.
"I felt sorry for the admin person who had to deal with it, the poor secretary or whoever that got the package," she said. "That's where my mind is, those who are directly involved with it."
Kurt Heinrich of the Vancouver School Board said no students at False Creek Elementary saw the package. He said the school board's crisis team would be on site in the morning.
"As you can imagine, it's a real challenging and shocking situation. Our priority is always first and foremost to maintain a calm and safe and protective environment for our students," said Heinrich.
At St. George's, staff patrolled the property Tuesday afternoon to ensure reporters did not enter the grounds.
St. George's spokesman Gordon Allan said police have told the school there does not appear to be any connection between the package and the school itself.
"At this point, there's been no connection made towards the school, there's no indication that anybody is at risk," said Allan.
"The police are saying it's a random act."
Foreign media dubbed Magnotta the "Canadian Psycho" after details emerged about the former porn actor.
The body parts that were discovered last week were mailed to the headquarters of the federal Conservative and Liberal parties. A foot arrived at the Conservative party headquarters, while the hand was intercepted while en route to the Liberal headquarters, police have said.
One of Lin's hands, a foot and his head were still missing, police said.
Cmdr. Ian Lafreniere told a Montreal news conference Tuesday investigators had obtained surveillance video of Magnotta allegedly mailing the gruesome packages to Ottawa from a Canada Post outlet in his Cote-des-Neiges neighbourhood.
Montreal police also spoke out about an infamous video they believe shows Lin's death and dismemberment. The footage was posted online.
The international manhunt for Magnotta ended with Monday's arrest after he was recognized inside the Berlin cafe, where he was reading online news articles about himself.
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