US President Donald Trump has accused Canada of being "very rough" with the United States on trade, defending his decision to impose new tariffs on softwood lumber from America's northern neighbour.

"People don't realise Canada has been very rough on the United States," he said while signing an executive order promoting American agriculture.

"Everyone thinks of Canada as being nice, but they've outsmarted our politicians for many years and you people understand that. So we did institute a very big tariff."

Canadian Prime Minister Justin Trudeau said Canada will respond firmly to Mr Trump after the US announced new tariffs on its softwood and vowed to also target Canadian milk.

"I'm polite, but I'm also very firm in defending Canada's interests," Mr Trudeau said in an interview with broadcaster CTV.

After targeting Canadian lumber yesterday, the US president threatened retaliation over pricing policies he said cut many US dairy farmers out of the Canadian market.

"We are going to engage respectfully but firmly with the US to demonstrate ... the scope of integration of our economies," Mr Trudeau said in response.

Softwood trade has long been an irritant between the two nations and was expected to flare up again after a deal that limited Canada's share of the US market expired in 2015.

But Mr Trump's hard line appears to have surprised Canada.

"We will work constructively together" to try to find solutions to these trade disputes, Mr Trudeau said, while downplaying Mr Trump's strong rhetoric.

Cross-border disputes over dairy and lumber, he said, have been "going on since before my father was prime minister" (from 1968).

"These are recurring challenges in what is a very big and complex Canada-US relationship," he said.

Earlier, Natural Resources Minister Jim Carr said Canada was preparing aid for forestry companies and rural communities that will be impacted by the US duties, while holding out hope for a negotiated settlement.

Mr Carr said Ottawa has put forward "reasonable proposals" over the past year addressing US producers' concerns.

He said Canada is prepared to agree to an import quota, for example, in exchange for "stable and predictable" US market access for its softwood.

"We will continue to press our American counterparts to rescind this unfair and unwarranted trade action," he said.

Canada has the world's third-largest forest canopy, and is the largest producer of softwood, the bulk of which goes to the United States.

This is the fifth trade row in more than three decades between the two nations over softwood. Independent trade panels have sided with Canada in all four of the previous cases.