More than 40 people illegally crossed the U.S. border and claimed refugee status within Quebec this past weekend, while 21 others did the same in Manitoba, border officials say.

The influx of asylum seekers from the United States comes as Prime Minister Justin Trudeau arrives at the White House on Monday for his first meeting with U.S. President Donald Trump. Mr. Trump last month signed an executive order that temporarily banned Syrian refugees and immigrants from seven Muslim-majority countries.

Patrizia Giolti, a Canada Border Services Agency spokesperson, in an e-mail Sunday said 42 people made refugee claims in Quebec over the weekend. Ms. Giolti did not say precisely where the refugee claimants crossed.

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The RCMP did not respond to messages seeking comment Sunday. A force spokesperson earlier said it had witnessed an increase in illegal border crossings in Quebec, Manitoba, and British Columbia, with the largest of those increases in Quebec.

Mr. Trudeau said last week his government was "very concerned" about the rise in asylum seekers. He emphasized the need to protect both migrants and Canada's border.

Refugee lawyer David Matas said Sunday when police discover migrants crossing into Canada they take them to the CBSA, which then screens them for security reasons but does not detain the migrants simply for entering the country at an unguarded area.

He said he has had a number of clients from Somalia who crossed into Canada, avoiding the ports-of-entry.

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"They have dramatic stories," he said in an interview. "They start off in Somalia. Then they'll go to Djibouti, Kenya, and all the way down to South Africa. Sometimes they have a lot of trouble in South Africa because there's a lot of xenophobia there. Brazil is often a destination … and then they just come north from there traversing all the Latin American countries. And eventually they end up in Canada."

CBSA did not provide annual totals for refugee claimants in Quebec.

But it has said the number of refugee claimants crossing into Manitoba so far in the 2016-17 fiscal year is over 400, up from 68 in 2013-14. Most were from African countries, particularly Somalia.

Unlike the United States, Canada will not deport failed refugee claimants to Somalia because the country is deemed too dangerous, Mr. Matas said.

"People here without status are not guaranteed to stay indefinitely. They're just here supposedly temporarily," he said.

Though CBSA and the RCMP said the largest increase in asylum seekers was in Quebec, much of the attention in recent days has been paid to crossings in Manitoba, with migrants arriving in the town of Emerson, population 700.

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Greg Janzen, Emerson's reeve, in an interview Sunday said he does not expect the increased arrivals to stop any time soon.

All 21 people who arrived in Emerson this weekend showed up Saturday morning. Mr. Janzen said it was unclear why no one arrived Sunday. On the previous Saturday, the RCMP stopped 19 people who had crossed the border.

The lawyer for two men from Ghana who passed through Emerson just before Christmas has said they lost fingers to frostbite.

Mr. Janzen said there is worry among locals that some of the people attempting to cross into Emerson might not have survived.

"That's another coffee-shop discussion," he said.

" … That possibility is real. They have been coming across when there's wind chills of -35. … I'd hate to be a farmer all of a sudden finding somebody dead laying there on the side of his field."

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Emerson officials met with the RCMP, CBSA and representatives from the federal and provincial governments on Thursday to address the community's concerns. Mr. Janzen said after the meeting, he was given assurances Emerson would receive support from other levels of government.

He said Sunday he was satisfied with that level of support.

Migrants who cross at open fields or other unguarded areas are not covered by the Canada-U.S. Safe Third Country Agreement, and have the right to make a refugee claim in Canada.

The safe-third-country agreement requires refugee claimants to apply for status in the country they arrive in first. The United States is the only country with which Canada has such an agreement. A Canadian government website says that that is partly because the United States meets a high standard of human rights.

At a minimum, all refugee claimants on Canadian soil are entitled to an oral hearing and fair procedures, under the Supreme Court's 1985 Singh decision establishing modern refugee rights in Canada, according to Efrat Arbel, who teaches law at the University of British Columbia's Allard Law School.

At the refugee hearings in Canada, a migrant's entry through a safe third country is irrelevant, Prof. Arbel said.

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"It doesn't matter how you've entered. Once you make your way in you advance your refugee claim as usual," she said. "If you've entered through a field, then the safe-third-country agreement wouldn't be attached to your claim. You're not obligated to disclose the manner by which you have entered."

She said the safe-third-country agreement creates an incentive for unauthorized border crossings. "It therefore not only puts the lives and safety of refugees at risk, it also makes our border less secure, more disorderly, more dangerous," she said.

A group of 235 Canadian legal scholars has called on the federal government to halt the safe-third-country agreement. A recent report by the Harvard Immigration and Refugee Clinic argued the United States can no longer be considered a "safe" country for refugees.