President Trump signed an order imposing stiff and sweeping new tariffs on imported steel and aluminum at the White House on Thursday. Credit Doug Mills/The New York Times

WASHINGTON — President Trump defied opposition from his own party and protests from overseas on Thursday as he signed orders imposing stiff and sweeping new tariffs on imported steel and aluminum. But he sought to soften the impact on America’s closest allies with a more flexible plan than originally envisioned.

After a week of furious lobbying and a burst of last-minute internal debates and confusion, Mr. Trump agreed to exempt, for now, Canada and Mexico and held out the possibility of later excluding allies such as Australia. But foreign leaders warned of a trade war that could escalate to other industries and be aimed at American goods.

“The actions we are taking today are not a matter of choice; they are a matter of necessity for our security,” Mr. Trump said in a ceremony at the White House where he officially authorized the tariffs, which will go into effect in 15 days.

Flanked by a handful of steel and aluminum workers, some wearing coveralls and holding hardhats, Mr. Trump presented his move as a way to rebuild vital industries decimated by foreign competition. “Our factories were left to rot and to rust all over the place; thriving communities turned into ghost towns,” he said. “The workers who poured their souls into building this great nation were betrayed. But that betrayal is now over.”

The orders represented Mr. Trump’s most expansive use of federal power to rewrite the rules of global trade since he took office and upended the prevailing consensus on free markets that has largely governed Washington under administrations of both parties for decades. A longtime critic of globalization, Mr. Trump argued that the United States has been ravaged by unfair trading partners.

As a result of Mr. Trump’s action, levies on foreign steel will rise by 25 percent and on imported aluminum by 10 percent. Business groups have warned that the impact could be felt across the supply chain as consumers face higher prices for automobiles, appliances and other consumer goods. But Mr. Trump’s aides dismissed such predictions as “fake news” and said most Americans will hardly notice any impact.

The United States is the largest steel importer in the world and the order could hit South Korea, China, Japan, Germany, Turkey and Brazil the hardest. Mr. Trump said his tariff orders were tailored to give him the authority to raise or lower levies on a country-by-country basis and add or take countries off the list as he deems appropriate.

The potential for an exemption is likely to trigger a tsunami of lobbying and cajoling as foreign governments pressure the White House for a carve-out. The United States imports steel from Japan, Germany, Brazil, South Korea and other nations.

In language authorizing the tariffs, the White House said any nation “with which we have a security relationship is welcome to discuss with the United States alternative ways to address the threatened impairment of the national security caused by imports from that country.”

The tariffs would be lifted if a country arrives “at a satisfactory alternative means to address the threat,” the order said.

Canada and Mexico would be exempt pending discussions with both countries about changes that would address Mr. Trump’s concerns about steel and aluminum and no time limit was imposed on the exclusion, although administration officials said they expect to deal with those two countries in short order.

Mr. Trump tied the exclusions to renegotiation of the North American Free Trade Agreement, which remains bogged down in inconclusive talks, but aides said national security concerns would be important in deciding whether to make the exclusions permanent.

Mr. Trump indicated that the tariffs would go into effect on Canada and Mexico “if we don’t make the deal on Nafta and if we terminate Nafta because they are unable to make a deal that’s fair.”

During a cabinet meeting earlier in the day, Mr. Trump singled out Australia as an example of another country that could be excluded, citing the trade surplus that the United States maintains with Australia, which imports more from America than it exports to the country.

Mario Draghi, the president of the European Central Bank, said on Thursday that a plan to impose broad tariffs that hit allies was “dangerous” and could undermine national security.

“If you put tariffs against your allies,” Mr. Draghi said at a news conference in Frankfurt, “one wonders who the enemies are.”

The president’s comments came after a frenzied and uncertain morning in which administration officials tried to resolve debates and complications that threatened to hold up an order he has been trumpeting for a week.

More than 100 Republican lawmakers sent a letter to Mr. Trump on Wednesday imploring him to drop plans for sweeping tariffs. Their letter came a day after Mr. Trump’s chief economic adviser, Gary D. Cohn, announced his resignation after his failure to forestall the president from pursuing tariffs.

Senator Ron Johnson, a Republican who represents the Midwestern industrial state of Wisconsin, which was key to Mr. Trump’s Electoral College victory in 2016, said a broad tariff plan would be self-destructive.

“If it’s targeted toward China, depending on how it’s tailored, I may not have a problem with it, because that’s where the root cause of the problem is, the gross oversupply within China,” Mr. Johnson said on CNN on Thursday. “But a generalized tariff that would actually harm allies, harm American consumers, by the way, harm American workers that use steel in production, hurting their competitive nature in global markets as well, I’m opposed to that.”

There was some bipartisan concurrence on the idea of focusing any tariff plan on China rather than more broadly. “President Trump has identified the right opponent — China — much better than both the Obama and Bush administrations did,” Senator Chuck Schumer of New York, the Democratic minority leader, said on the floor.

“But I would say to you, Mr. President, don’t swing blindly and wildly at our foe, China,” he added. “Establish a well-placed jab at China. Set them back. Let them know we mean business. President Trump ought to rethink his plan so it actually achieves what he says he wants it to achieve.”

While many economists have said it is natural for a high-technology, highly developed economy like the United States to evolve away from raw industries, Mr. Trump presented the steel and aluminum sectors in romantic terms, signs of a muscular superpower that has been allowed to atrophy under his predecessors.

“Steel is steel,” he said. “You don’t have steel, you don’t have a country.”

He invited a few of the steelworkers to make comments and they told stories of plants that have cut back or idled altogether. “These tariffs going into place, this gives us the ability to come back to 100 percent capacity,” one said.

The issue has divided Mr. Trump’s own team, however, as more nationalist and protectionist wing led by Wilbur Ross, the commerce secretary, and Peter Navarro, the president’s trade and manufacturing adviser, overcame objections from Wall Street advisers like Mr. Cohn, previously a Goldman Sachs banker. Even national security officials like Defense Secretary Jim Mattis cautioned Mr. Trump about the plan, fearing it would roil relations with key security allies.

The consequences of the split were on display at the cabinet meeting earlier in the day when Mr. Trump thanked Mr. Cohn for his service, but needled him about his decision to leave. “He may be a globalist, but I still like him,” the president said as Mr. Cohn sat in a chair along the wall and smiled. “He’s seriously a globalist. There’s no question. You know what? In his own way he’s a nationalist, because he loves his country.”

Mr. Trump then suggested that Mr. Cohn might eventually return to the administration. “I have a feeling you’ll be back,” the president told him. In a teasing voice, he added: “I don’t know if I can put him in the same position though. He’s not quite as strong on those tariffs as we want.”