OTTAWA (Reuters) - Most of the people crossing the U.S. border into Canada to claim asylum had been in the United States legally, and Canada is sharing their information with U.S. authorities to help understand the phenomenon, a top official said on Friday.

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Several hundred asylum seekers, mainly from Africa but also the Middle East, have entered Canada. The refugees and migrant agencies blame the exodus on moves by U.S. President Donald Trump to clamp down on immigration.

“We have provided information about the specific documents that were presented at the border because those are American documents,” Canadian Public Safety Minister Ralph Goodale told reporters.

Goodale spoke after meeting U.S. Homeland Security Secretary John Kelly in Ottawa for talks on the influx, which is putting domestic pressure on Prime Minister Justin Trudeau.

Emergency responders and the Royal Canadian Mounted Police are struggling to respond to people defying wintry conditions to cross the undefended border near Emerson, Manitoba.

Manitoba premier Brian Pallister is demanding Trudeau’s Liberal government provide money and resources.

Ottawa says there is a chance the flow of people will increase as the weather improves.

“We obviously have safety concerns on both sides of the border,” Goodale said, adding that he had seen no evidence yet of any profiteering or human trafficking.

Kelly told CTV that he and his Canadian counterparts were “perplexed as to why people who generally, as a group, have come to the United States legally” would make their way north.

Canadian officials caution against the idea that Trump’s policies are solely to blame. Goodale said some of the asylum seekers had been planning their move in early 2016, months before the November election that brought Trump to power.

Goodale said there was little Canada could do, since the “vast majority” of those crossing the border had been in the United States legally and enjoyed freedom of movement.

“No one is suggesting the construction of a wall along the Canadian border, no one is saying the RCMP should line up along the border and join arms and shoo people away,” he said.

Goodale said he and Kelly had agreed officials needed to gather more information to work out what was happening.

Factors to look at, he said, included “who are the people involved in this migration, where did their journey begin ... (and) how is the migration being accomplished?”