A proposal to station troops at the US-Canada border would damage relations between the two countries, Canadian Prime Minister Justin Trudeau said.
Mr Trudeau was speaking after the Trump administration was reported to be considering the move to match deployments along its border with Mexico.
The Wall Street Journal has since reported the idea has been dropped.
Mr Trudeau said his government had been in discussions with the White House seeking to persuade the US not to go through with the idea.
“Canada and the United States have the longest un-militarised border in the world and it is very much in both of our interests for it to remain that way,” he said.
Mr Trump said: “We have a lot of things coming in from Canada, we have trade, some illegal trade, that we don’t like.”
According to a US official, the Department of Homeland Security did make a formal request to the Pentagon for military forces to provide additional security along the northern border, between entry points.
The official said the request was made a few days ago and the Defence Department had done some initial planning but there was no final decision on whether or not to approve the request.
As our next Ambassador to the US, @KirstenHillmanA will build on the strong relationship between our two countries. And at a time when all countries must work together to fight COVID-19, this could not be more important. Get the details on her appointment: https://t.co/tssP8esaUL pic.twitter.com/XExO3QYZhj
— Justin Trudeau (@JustinTrudeau) March 26, 2020
Canadian Deputy Prime Minister Chrystia Freeland said the government had told the Trump administration there was no justification for troops.
Very few people cross the border into the US from Canada illegally and Canada has universal health care and widespread testing for the virus.
She said: “What we have said is, ‘We really do not believe at all that there would be a public health justification for you to take this action,’
“And we have said, ‘We really don’t think this is the right way to treat a trusted friend and military ally.'”
Bruce Heyman, a former US ambassador to Canada, said it would be a serious misuse of resources and a dangerous and inappropriate use of American troops.
“It makes no military sense. It makes no economic sense. It makes no sense at any level other than Donald Trump’s political level,” he added.