The plan has also provoked a sharp backlash from members of the president’s own party and industries that could be hurt by rising prices as a result of the tariffs. In the days since the announcement, opponents have fiercely lobbied the administration to abandon or scale back the measure.

“There is a lot of concern among Republican senators that this could sort of metastasize into a larger trade war,” Senator Mitch McConnell, the majority leader and Republican of Kentucky, told reporters at the Capitol on Tuesday. “Many of our members are discussing with the administration just how broad, how sweeping, this might be.”

The president has said there may be exceptions. On Monday, he floated the idea of exempting Canada and Mexico if the countries made concessions in a renegotiation of the North American Free Trade Agreement.

At a news conference on Tuesday, the president said the European Union could be exempted if it removed some of the “horrible barriers” that prevent American products from entering its market. “Otherwise, we’re going to leave it as it is,” Mr. Trump said, referring to the tariff plan.

Yet some trade advisers say the administration is unlikely to consider such an exemption for South Korea, which several officials in the White House see as one of biggest global culprits in trade.

That view has stunned the South Korean government, which is used to working closely with the United States on economic and security matters. The United States maintains a large military presence in Seoul, the capital, and it has been a partner on issues like the North Korean nuclear threat and balancing against China’s rise in the Pacific.

Against the advice of many economists, the Trump administration sees the trade deficit with South Korea as a sign that the United States is on the losing end of their economic relationship. That is the major reason American officials have started to renegotiate the United States Korea Free Trade Agreement.