The Canadian government has sharpened its tone towards asylum seekers, warning that simply making it across the border is not a “free ticket” to Canada as the number of migrants crossing from the US continues to rise.

Since the election of Donald Trump, growing numbers of asylum seekers have been entering Canada by foot, driven by fears over the US president’s approach to immigration.

Last year more than 20,000 people entered Canada at remote, unguarded locations along the border, sometimes braving freezing temperatures, fields of waist-deep snow and icy ditches. Doing so allows migrants to skirt a longstanding pact that bars most refugee claimants in the US from applying for asylum in Canada.

The flow of people shows little sign of abating, with 7,300 people entering Canada irregularly this year – more than double the number of those who made the journey in the first four months of 2017.

This week, Canadian officials sought to tone down the welcoming image they have cultivated since coming to power, offering instead a blunt warning to those considering making the crossing into Canada.

“Coming across the border in a way that seeks to circumvent the law or defy proper procedure is no free ticket to Canada,” Ralph Goodale, the country’s public safety minister, said on Monday.

Officials said they believe that more than 90% of those entering Canada do not meet the criteria to be considered refugees. “They must prove they need Canada’s protection to keep them safe,” said Goodale. “Seeking asylum is not a shortcut to get around normal immigration rules and procedures.”

After rising to a high of about 250 people a day earlier this year, the flow of migrants – many of them Nigerian nationals – has stabilised to around 70 or 80 per day, said Goodale.

Canada’s immigration minister, Ahmed Hussen, said he would travel to Nigeria in the coming days to address the issue. Canada has been working with the United States to crack down on Nigerians who obtain tourist visas to the US solely for the purposes of walking into Canada to claim asylum, said Hussen.

The federal government has been under pressure to stem the flow of migrants across the border. Last month the opposition Conservatives – who have linked the rise in asylum seekers to Trudeau’s viral tweet welcoming refugees – tabled a motion in the House of Commons urging the government to take “immediate action” on the issue.

Canadians across the political spectrum are generally supportive of immigration, but the Conservative MP behind the motion argued that the issue, if not properly addressed, could cause Canadians to lose confidence in the system.

“My concern is that if the government does not take steps to rectify [its] failure to manage our borders, we are going to rapidly see Canadians lose that social licence for immigration, because there will be a lack of faith in the ability of the government to ensure planned and orderly migration,” said Michelle Rempel.

The New Democratic party and organisations such as Amnesty International have long urged the federal government to suspend the pact with the US that forces Canada to turn away most asylum seekers who attempt to enter the country at official border crossings.

Halting the Safe Third Country Agreement would allow asylum seekers to make claims at official ports of entry, reducing the dangers faced by migrants and allowing Canada better control over the process, they argue.

The province of Quebec – where the bulk of asylum seekers have arrived after crossing into Canada from the US – has called for more resources to help with the increase in refugee claimants.

David Heurtel, Quebec’s immigration minister, said last month: “This is not about money. This is about saying that Quebec can do its part, but our resources are completely saturated and we can’t do more.”