President Trump made one of the biggest gambles of his presidency Tuesday by initiating sweeping tariffs with no clear rationale on imports from Canada, Mexico and China, triggering a trade war that risks undermining the United States economy.

His actions have upended diplomatic relations with America’s largest trading partners, sent markets tumbling, and provoked retaliation on U.S. products — leaving businesses, investors and economists puzzled as to why Mr. Trump would create such upheaval without extended negotiations or clear reasoning.

Mr. Trump has offered up a variety of explanations for the tariffs, saying they are punishment for other countries’ failure to stop drugs and migrants from flowing into the United States, a way to force manufacturing back to America and retribution for countries that take advantage of the United States. On Tuesday, he cited Canada’s hostility toward American banks as another reason.

Canadian Prime Minister Justin Trudeau said it was difficult to understand Mr. Trump’s rationale for the tariffs but posited that his intent was to cripple Canada. “What he wants is to see is a total collapse of the Canadian economy, because that’ll make it easier to annex us,” Mr. Trudeau said during a news conference on Tuesday. “That’s never going to happen. We will never be the 51st state.”

Canada announced a series of retaliatory tariffs on $30 billion worth of American imports, and Mr. Trudeau said that other “non-tariff” measures were forthcoming.

“Yeah, he can do damage to the Canadian economy but he is going to rapidly find out, as American families are going to rapidly find out, it’s going to hurt people on both sides of the border,” Mr. Trudeau said.