In a post on his social media platform Tuesday morning, Mr. Trump wrote that Canadian steel and aluminum would face a 50 percent tariff, double what he plans to charge on metals from other countries beginning Wednesday. He said the levies were in response to an additional charge that Ontario had placed on electricity coming into the United States, which was in turn a response to tariffs Mr. Trump imposed on Canada last week.

By Tuesday afternoon, leaders had begun to relent. The premier of Ontario, Canada’s most populous province, said he would suspend the electricity surcharge, and Mr. Trump said at the White House he would “probably” reduce the tariff on Canadian metals.

Kush Desai, a White House spokesman, said Tuesday afternoon that Mr. Trump’s threats had succeeded in getting Canada to back down. “President Trump has once again used the leverage of the American economy, which is the best and biggest in the world, to deliver a win for the American people,” he said.

As a result, he said that Canada would face the same 25 percent tariff on metals as all of America’s trading partners will when they go into effect at midnight.

Still, that levy could reignite trade tensions. The Canadian government has vowed to retaliate against the 25 percent tariffs that Mr. Trump will introduce on global steel and aluminum on Wednesday.

“The Government of Canada has been clear on this issue since the beginning — should the United States move forward tomorrow with the imposition of tariffs on Canadian products, including steel and aluminum, we will be ready to respond firmly and proportionately,” said Gabriel Brunet, spokesman for Dominic LeBlanc, the finance minister who is leading Canada’s trade response.

Mr. Trump’s new confrontation with Canada tariffs sent jittery markets tumbling, with major indexes closing down for the day. In addition to doubling the metal tariffs, the president threatened more levies if Canada didn’t drop various tariffs it imposes on U.S. dairy and agricultural products.

“If other egregious, long time Tariffs are not likewise dropped by Canada, I will substantially increase, on April 2nd, the Tariffs on Cars coming into the U.S. which will, essentially, permanently shut down the automobile manufacturing business in Canada,” he threatened.

Mr. Trump went on to say that “the only thing that makes sense” is for Canada to become the 51st U.S. state. The idea of joining the United States has been angrily rejected across Canada.

The president reiterated those comments Tuesday afternoon, saying that Canada would no longer have a tariff problem if it became part of the United States.

“When you take away that artificial line that looks like it was done with a ruler,” he said, referring to the border, “and that’s what it was, some guy sat there years ago and they said, well, when you take away that, and you look at that beautiful formation of Canada and the United States, there is no place anywhere in the world that looks like that.”

Doug Ford, Ontario’s premier, said in a news conference in Toronto Tuesday afternoon that he would suspend the 25 percent surcharge on electricity exports to Michigan, Minnesota and New York that went into effect on Monday.

“The temperature needs to come down,” Mr. Ford said.

In a statement jointly issued with Howard Lutnick, the U.S. secretary of commerce, Mr. Ford said that the sides would meet in Washington on March 13, and discuss a “renewed U.S.M.C.A.,” referring to the trade agreement between Canada, Mexico and the United States, ahead of more tariffs to come on April 2.

Mr. Trump’s earlier comments significantly escalated a confrontation with one of America’s largest trading partners, and called into question his intentions.

Canadian officials first thought Mr. Trump’s idea of absorbing Canada into the United State was a joke, but they have more recently begun to take the president’s threats seriously.

Last week, outgoing Prime Minister Justin Trudeau of Canada called Mr. Trump’s ostensible reason for imposing tariffs on Canada — to stop the flow of fentanyl into the United States — “completely bogus.”

Mr. Trudeau suggested that what Mr. Trump wanted to see was a collapse of the Canadian economy “because that’ll make it easier to annex us.”

“That’s never going to happen,” he said.

Mr. Trump spent much of his social media post on Tuesday essentially cajoling Canada to become part of America, writing that it would make tariffs “totally disappear,” lower Canadian taxes and make the country more secure militarily.

In calls between Mr. Trump and Mr. Trudeau in early February, the American president told the Canadian prime minister that he did not believe that the treaty that demarcates the border between Canada and the United States was valid, according to people with knowledge of the conversations.

When questioned in a news conference in January about whether he planned to use military force to annex Canada, Mr. Trump replied that he would use “economic force.”

Last week, Mr. Trump hit Canada and Mexico with sweeping 25 percent tariffs on all imports, before walking some — but not all — of those levies back a few days later.

Mark Carney, who will succeed Mr. Trudeau as prime minister of Canada within the next few days, called the latest tariff threat “an attack on Canadian workers, families, and businesses” in a social media post.

He added: “My government will ensure our response has maximum impact in the US and minimal impact here in Canada. My government will keep our tariffs on until the Americans show us respect and make credible, reliable commitments to free and fair trade.”

Mr. Trump, in his post, also targeted the Canadian dairy industry, saying that the country “must immediately drop their Anti-American Farmer Tariff of 250% to 390% on various U.S. dairy products, which has long been considered outrageous.”

The Canadian dairy industry has become a frequent target of Mr. Trump’s in recent weeks, although his description of those barriers is misleading. Canada allows a certain amount of U.S. dairy products to come in to the country tariff-free, as long as they don’t exceed certain import quotas, which increase every year. After imports hit a certain level, they are hit with high tariffs, for example 298.5 percent for butter. The system is known as a “tariff-rate quota.”

For a variety of reasons, American dairy exporters, who shipped about $1.1 billion of their products to Canada last year, have never exceeded those quotas, so those tariffs have never been activated. The United States also has tariff-rate quotas for some dairy imports, and other goods, though its tariffs tend to be much lower.

Mr. Trump also said Tuesday that he would declare “a national emergency on electricity within the threatened area” that would “allow the U.S. to quickly do what has to be done to alleviate this abusive threat from Canada.”

“They will pay a financial price for this so big that it will be read about in History Books for many years to come!” he said in a subsequent social media post.

Ryan Young, a senior economist at the Competitive Enterprise Institute, said that putting tariffs on foreign countries’ goods would almost always incite them to retaliate, increasing costs for consumers and worsening concerns about a recession. “Sometimes the only way to win is not to play,” he said. “This is true of nuclear war, and it is true of tariffs.”

Mr. Trump’s head-spinning tariff threats and quick reversals against America’s largest trading partners have caused anxiety for investors and businesses. The president imposed a 25 percent tariff on imports from Mexico and nearly all imports from Canada last Tuesday.

But Mr. Trump partly lifted the measure after stock markets sank and various industries pushed back. By Thursday, the president suspended those tariffs indefinitely for all products that comply with the North American free trade deal, U.S.-Mexico-Canada Agreement, or U.S.M.C.A. — about half of all imports from Mexico and nearly 40 percent of those from Canada.

The president has repeatedly promised that more tariffs are on the way. He has said that he would impose tariffs on foreign cars as well as “reciprocal” tariffs on foreign nations on April 2.

Eswar Prasad, a professor of trade policy at Cornell University and a former official at the International Monetary Fund, said that the threats against Canada would have important repercussions not just for the North American economies “but for the stability of the world order.”

“Trump’s aggressive tariff actions against a country long seen as a close U.S. economic and geopolitical ally puts the entire world on notice that strong historical relationships are no guarantee of future cordiality,” he said.

Matina Stevis-Gridneff and Danielle Kaye contributed reporting.