Justin Trudeau at the Broadway premiere of a musical, Come From Away, celebrating Canada's welcome to stranded travellers after the September 11 attacks

Justin Trudeau has sought to tone down the warm welcome he promised to migrants, after arrivals at the Canadian border hit 250 a day, leaving immigration officials struggling to cope with the influx.

The Canadian prime minister tweeted shortly after President Donald Trump announced the halt of the US refugee programme that Canada would still be a haven.

“To those fleeing persecution, terror & war, Canadians will welcome you, regardless of your faith. Diversity is our strength #WelcomeToCanada,” he said.

To those fleeing persecution, terror & war, Canadians will welcome you, regardless of your faith. Diversity is our strength #WelcomeToCanada — Justin Trudeau (@JustinTrudeau) January 28, 2017

But since the start of the year more than 11,300 people have crossed into Canada by foot from the US, with the surge due in large part to fears about Mr Trump’s immigration policy.

Canada is on track to record the most refugee claims in a decade.

The majority – around 85 per cent, according to Canadian officials – are from Haiti. In May Mr Trump floated the idea of rescinding a long-standing agreement to allow Haitians to remain in the country, meaning that a possible 58,000 Haitians could be deported in 2018.

“For someone to successfully seek asylum it’s not about economic migration,” said Mr Trudeau, in an attempt to make economic migrants reconsider.

Asylum seekers unload their belongings from a truck at a processing centre near the Canada-United States border in Lacolle, Quebec Credit: Graham Hughes/The Canadian Press via AP

“It’s about vulnerability, exposure to torture or death, or being stateless people. If they are seeking asylum we’ll evaluate them on the basis of what it is to be a refugee or asylum seeker.”

More than 6,000 people have skirted border checkpoints to enter Canada since the start of July.

Overwhelmed by these numbers, the government has increased patrols along the border and added immigration staff to process claims. Montreal’s Olympic stadium has been turned into a temporary welcome center, and the military has been deployed to set up a 500-person camp on the border.

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Asylum seekers are shown next to tents at the Canada-United States border in Lacolle, Quebec Credit: Graham Hughes/The Canadian Press via AP

“You will not be at an advantage if you choose to enter Canada irregularly,” said Mr Trudeau.

“You must follow the rules, and there are many.”

Critics have accused Mr Trudeau of encouraging would-be refugees to come to Canada without thinking through the consequences.

Michelle Rempel, a politician from the opposition Conservative Party, said it was "completely ridiculous that the Prime Minister of Canada would tout a tent city" to deal with the influx as winter approached.