Local officials say the incident is unusual since in the past people have tried to cross into Canada from the United States, rather than the other way round.
Prime Minister Justin Trudeau has promised Canada is doing all it can to stop people smuggling across the US border after a family of four froze to death in a "mind-blowing" tragedy.
A man, woman, baby and teenager were found dead in the province of Manitoba, a few yards north of the frontier with Minnesota.
"It was an absolutely mind-blowing story. It's so tragic to see a family die like that, victims of human traffickers ... and of people who took advantage of their desire to build a better life," Trudeau told a news conference on Friday.
"This is why we are doing all we can to discourage people from crossing the border in an irregular or illicit manner. We know there are great risks in doing so," he continued.
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Working close with US
Canada, Trudeau said, was working very closely with the United States to stop smuggling and help people "taking unacceptable risks".
US authorities have charged a US man with human trafficking after the incident.
The four have tentatively been identified as a family from India, part of a larger group trying to enter the United States by walking across snow-covered fields in a remote region.
Local officials said the incident was unusual since in the past, people have tried to cross into Canada from the United States, rather than the other way round.
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