Canadian consulates in the United States have been told to set the record straight about Canada's immigration policies as the flow of asylum seekers continues unabated.

"We have mobilized them to get in touch with different groups that might be considering coming to Canada so they can clearly explain the rules in place and the criteria that must be met before being able to come," said Transport Minister Marc Garneau.

His comments come as asylum seekers continue to arrive at the Quebec-New York border.

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Related: As asylum seekers flock to Quebec, Canadian agencies pitch in

About 3,000 of them, the majority Haitian, have crossed on foot in recent weeks in an attempt to gain refugee status.

The influx has been so great the Canadian Forces have built two temporary shelters with electricity and heating near the border, with a third planned that would bring the total capacity to 1,200 people.

Garneau said Monday all 13 Canadian consulates in the United States will aim to educate those thinking of crossing on foot.

In the United States, the Trump administration is considering ending a program that granted Haitians so-called "temporary protected status" following the massive earthquake that struck in 2010.

Groups that work with migrants say those spilling across the border are fearful of being returned to an uncertain future in Haiti as early as next January.

But Garneau said asylum seekers, to be considered refugees, must prove there's a risk if they're returned to their native countries.

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Garneau said he gave an interview to the Miami Herald on Sunday to push that same message to the Haitian diaspora living in Florida.

For her part, Quebec Immigration Minister Kathleen Weil told Radio-Canada she welcomes the co-ordination of the message.

The province must provide basic services to asylum seekers on its territory and has stretched housing and resources in the Montreal area.

Numerous temporary shelters have been set up, including at the Olympic Stadium and the former Royal Victoria Hospital building, to house asylum seekers on a temporary basis.

Many asylum seekers are ferried to Montreal after a few days at Saint-Bernard-de-Lacolle, while they undergo an initial vetting.

Without going so far as to promise financial compensation, Garneau said Ottawa was aware the situation has "imposed additional needs on the Quebec government."