Trump says tariff exemptions for Canada, Mexico depend on 'new and fair' trade deal

President Donald Trump said Monday "we're not backing down" on steep tariffs he pledged last week to impose on steel and aluminum imports - even for U.S. neighbors Canada and Mexico.

"No, we're not backing down," Trump said at an Oval Office meeting with Israeli Prime Minister Benjamin Netanyahu. "We've had a very bad deal with Mexico, a very bad deal with Canada -- it’s called NAFTA. For many years, NAFTA’s been a disaster.”

And when asked whether the tariffs might trigger a trade war, Trump dismissed the prospect. “I don’t think so,” Trump said. “I don’t think we’re going to have a trade war.”

But in a noteworthy break with the president, a fellow Republican, House Speaker Paul Ryan, warns just the opposite.

"We are extremely worried about the consequences of a trade war and are urging the White House to not advance with this plan," Ryan's spokeswoman AshLee Strong said in a statement Monday. "The new tax reform law has boosted the economy and we certainly don't want to jeopardize those gains.”

In tweets earlier Monday, Trump also doubled down on his pledge to enact the new tariffs, saying any exemptions for border countries Canada and Mexico would be part of "new and fair" trade agreements.

The North American Free Trade Agreement, or NAFTA, is now nearing the end of a year-long renegotiation.

"But if I do make a deal which is fair to the workers and to the American people, that would be, I would imagine, one of the points that we'll negotiate," Trump elaborated in his Oval Office comments. It will be tariffs on steel for Canada and for Mexico. So we'll see what happens."

"But right now, 100 percent, but it could be a part of NAFTA. And I understand I just got a call from the people who are right now in Mexico City negotiating NAFTA, Mexico and really Canada want to talk about it. But if they aren't going to make a fair NAFTA deal, we're just going to leave it this way." Trump said.

Trump announced his plans to impose a 25 percent tariff on imported steel and a 10 percect tariff on imported aluminum late last week, during a meeting with Secretary of Commerce Wilbur Ross and industry executives.

"It'll be for a long period of time,” the president said about the proposed tariffs, which he said were being written and would be signed this week. "We’re going to build our steel industry back, we’re going to build our aluminum industry back."

The announcement was linked to steep drops in the stock market at the end of last week. Some Republican lawmakers criticized the deal, fearing increased costs to American consumers.

Some Democratic lawmakers heralded the deal for protecting American industries.

Others expressed concern that such a policy could launch a global trade war, following rebukes from the officials in Canada, China, the European Union and other countries.

But Commerce secretary Ross dismissed that notion in an interview with ABC News Chief Anchor George Stephanopoulos on "This Week" Sunday.

"It's some $3 billion of goods that the Europeans have threatened to put [tariffs] on," the commerce secretary said. "Well, in our sized economy, that's a tiny, tiny fraction of one percent. So while it might affect an individual producer for a little while, overall it's not going to be much more than a rounding error."

Chrystia Freeland, Canada's minister of foreign affairs, released a statement in response to the proposal last week.

"Canada would view any trade restrictions on Canadian steel and aluminum as absolutely unacceptable," the statement read.

"Any restrictions would harm workers, the industry and manufacturers on both sides of the border," Freeland said. "The steel and aluminum industry is highly integrated and supports critical North American manufacturing supply chains. The Canadian government will continue to make this point directly with the American administration at all levels."

But on "Fox and Friends" Monday morning, White House trade adviser Peter Navarro made it clear that the president is still pursuing the tariffs for all countries.

He reiterated the levels proposed, saying, "25 percent on steel and the 10 percent on aluminum -- no country exclusions, firm line in the sand."