WASHINGTON — Nearly a year after imposing stiff tariffs on foreign metals, the United States is pressing Canada and Mexico to agree to permanent limits on the amount of steel and aluminum they export to America each year.

The demand, reiterated in meetings with Canadian officials this week, has been rejected by Canada and Mexico and is eliciting opposition from American companies that use foreign steel and aluminum in their products.

The dispute is further complicating efforts to finalize a new North American Free Trade Agreement, which faces a long battle in Congress and must be ratified by legislators in all three nations. Canada and Mexico had hoped that President Trump would remove the tariffs last year, when the three countries agreed on a new trade deal known as the United States-Mexico-Canada Agreement. That did not happen, and Mexico and Canada are now demanding that the United States drop the levies as a condition of ratifying the deal.

But Mr. Trump’s advisers appear hesitant to do away with what they see as a source of leverage with Canada and Mexico. Democrats, who now control the House, have made clear they will not approve the new agreement without changes that could require all three countries to sign off, and the White House may use the tariffs as a cudgel to force Canada and Mexico to agree to any alterations.