The premier of Manitoba, whose province is grappling with asylum seekers risking life and limb in frigid weather to come to Canada, says Prime Minister Justin Trudeau can play a role in resolving the crisis by raising the issue of illegal border crossings with U.S. President Donald Trump.

Recent decisions by the Trump administration are likely to increase the number of refugees arriving in Canada, Brian Pallister told CBC Radio's The House host Chris Hall in an interview airing Saturday.

The Progressive Conservative leader said the issue should be raised tactfully. "But it must be raised. Because this is an issue, I think, that's not likely to go away," he said.

"The United States has a deserved reputation as well for being a very open society. That Statue of Liberty didn't have blinders on it, so it's important that there be some discussion about the nature of what is going on in that country in recent days and weeks."

Trudeau and Trump discussed border co-operation during a phone call Thursday, but it's not clear if the issue of illegal border crossings was broached.

According to a statement issued by the White House, "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."

More co-operation needed, says Pallister

Pallister has said he's sent a letter to the federal government with "specific issues" he'd like Ottawa to address when it comes to handling the number of migrants crossing into Canada from the U.S.

"We're not suggesting that it be the best way to seek entry into a country. No one is suggesting that. But the reality is people are coming here. They are crossing fields in the middle of winter at great risk to themselves because they are hopeful this is their future," he said.

The premier said he's also trying to co-ordinate talks with his counterparts in neighbouring North Dakota and Minnesota to talk more about what needs to happen on both sides of the border.

Refugees Border 20170209

A sign is posted near Emerson, Man., where refugees have been crossing the border illegally into Canada. (John Woods/Canadian Press)

"Minnesota, of course, is home to a significant population of Somalis who have escaped hopelessness, as they view it, in their own country of origin. They have contacts here and those connections tell me the likelihood of an additional influx from Minneapolis-Saint Paul continues to be very real," he said.

On Thursday, Pallister's government announced more aid for refugees, while pushing the federal government to better co-ordinate and communicate with the provinces.

"This is not likely a problem or a challenge that is going to go away very soon, so we need to co-ordinate our approaches," he said.