Candidate David Popescu told some 200 students Tuesday afternoon at Sudbury Secondary School "God would hurt" those who had an abortion, Sun Media reported.
Soon afterward, a student asked Popescu's opinion of gay marriage, to which he responded homosexuals should be executed, the report said.
It wasn't reported who contacted the Greater Sudbury Police Service to complain of hateful speech, but Sun Media said Popescu repeated his statement in a telephone interview.
"A young man asked me what I think of homosexual marriages and I said I think homosexuals should be executed," he said. "My whole reason for running is the Bible and the Bible couldn't be more clear on that point."
Deputy Police Chief Frank Elsner told the news agency the complaints were being taken seriously.
"We are actively conducting a criminal investigation in this matter," he said.
Canada's federal election is scheduled for Oct. 14.