Justin Trudeau, Canada’s prime minister, is facing growing political pressure to address the steady stream of asylum seekers who have been braving freezing temperatures, fields of waist-deep snow and icy ditches to cross into Canada from the US by foot.

Recent months have seen a growing number of people entering Canada at remote, unguarded locations along the US border. Doing so allows the migrants – many of whom are desperate to flee Trump’s crackdown on immigration – to skirt a longstanding pact that bars most refugee claimants in the US from applying for asylum in Canada.

Advocates in Manitoba say they know of some 139 refugees – including children – who have made the perilous crossing since the start of the year, while groups in Quebec, British Columbia and Ontario also report a rise in irregular crossings.

Some haul suitcases for hours across frozen fields that straddle the border, while others are dropped by taxis metres away from the Quebec border. The asylum seekers – many of whom are from Somalia, Ghana and Djibouti – say their actions are driven by fears of what a Donald Trump presidency could mean for refugees in the US.

As photos of Canadian police smiling as they greeted migrants made the rounds on social media, Trudeau said this week that the government would not seek to stem irregular migration along the US border.

“One of the reasons why Canada remains an open country is Canadians trust our immigration system and the integrity of our borders and the help we provide people who are looking for safety,” Trudeau told parliament. “We will continue to strike that balance between a rigorous system and accepting people who need help.”

Amid concerns that the number of people attempting the crossing could spike as the weather warms, the opposition Conservatives have called on Trudeau and his government to do more to halt the flow of irregular migrants.

Conservative MP Steven Blaney urged Canadian officials to hand over irregular migrants to US authorities while his colleague Candice Bergen highlighted concerns about safety. “People running across farmers’ fields illegally cannot continue,” Bergen said recently. “It is not safe for the people who are running across the fields. It is not safe for the community.”

In the small border town of Emerson, Manitoba – where dozens of refugee claimants have arrived in recent months – Conservative MP Ted Falk pointed to the town’s stretched resources. Emerson’s emergency response team and volunteer firefighting crew have been regularly woken in the middle of the night to help the asylum seekers, Falk said in a video posted to social media.

“We all know that Canada is generous and accepting,” he added. “But we also need to ensure that the integrity of our borders is protected and that we look after our national security. We need to know who is coming into our country, where they’re coming in and why.”

The progressive New Democratic party has repeatedly called on Trudeau’s government to immediately suspend the agreement that prohibits most migrants in the US from making a refugee claim at Canada’s official border crossings.

Under the 2004 Safe Third Country Agreement between Canada and the US, migrants must apply for asylum in the first country in which they arrive. The agreement is applied at official land, train and airport border crossings.

Advocates say the agreement is leading migrants to instead attempt to enter Canada at isolated, unguarded locations. Once they reach Canadian soil, the agreement no longer applies. The migrants, often disoriented and cold, are apprehended by police and have the right to make a refugee claim and have it heard by Canadian authorities.

The agreement hinges on the idea that the US is a safe country for refugees – an assumption that clashes with the stark reality of the Trump administration, said New Democratic MP Jenny Kwan. “When you have a country that has declared that you’re banned, that you’re not welcome and we don’t want you, and because of where you come from, because of your race and because of your religion, do you feel safe there?” Kwan recently told parliament.

“Under those circumstances, shouldn’t we immediately suspend the agreement?” Doing so would allow the migrants to request refugee status at Canada’s official border crossings.

Several organisations, from Amnesty International to the Canadian Council for Refugees, as well as hundreds of legal experts in Canada and the US are also urging Canada to scrap the pact.

So far, the Canadian government has said it has no plans to suspend the agreement.

The influx of irregular migrants is being closely monitored by the Royal Canadian Mounted Police and border officials, Ralph Goodale, Canada’s public safety minister, said this week. “They have made some rearrangements in the deployment of their resources to make sure that they can deal effectively with the situation.”

After months of reports of people crossing his province’s borders, the premier of Manitoba recently called on the federal government to put in place a national strategy to deal with the influx.

While his government will continue to greet those who arrive with “open arms and open hearts”, Brian Pallister said Trudeau’s government must do more to address the issue. “I see an opportunity here for the federal government that they are not yet pursuing, to improve the way we do things and help make sure we are addressing a situation that some would fear is getting somewhat out of hand.”

In an interview with the Canadian Broadcasting Corporation, he called on Trudeau to find a tactful approach to broach the issue with Trump. “But it must be raised. Because this is an issue, I think, that’s not likely to go away,” said Pallister.

The issue of border cooperation was raised during a phone call between Trudeau and Trump on Thursday. It was not made clear whether the issue of refugees crossing irregularly into Canada was highlighted, but the White House noted in a statement that: “President Trump emphasized the importance of working closely with Canada on cross-border issues, including implementation of his administration’s actions to protect America from terrorist attacks by foreign nationals and others.”