WASHINGTON — A potential deal to ease President Trump’s metal tariffs on Mexico and Canada is being complicated by the Trump administration’s push to place strict quotas on imported steel from the two trading partners.

Canada and Mexico have been pushing for the removal of Mr. Trump’s 25 percent steel and 10 percent aluminum tariffs ahead of the ceremonial signing of the revised North American Free Trade Agreement this month at the Group of 20 summit meeting in Buenos Aires. While the three countries reached a new trade pact in September, the metal tariffs have remained in place, and Canada and Mexico have been pressing the White House to relax the levies before the United States-Mexico-Canada Agreement is signed.

The White House could ultimately lift the aluminum tariffs, but the administration still wants to impose limits on foreign steel to prevent a flood of cheap metals into the United States, according to people briefed on the discussions. American trade negotiators are proposing a quota system that would cap the volume of steel Canada and Mexico can export to the United States each year. The countries are also discussing an agreement that would bolster efforts to combat dumping of cheap metals from China, which has been a source of ire for all three nations.

American trade officials have made some progress in securing an agreement with Mexico, which is eager to eliminate the lingering threat the metal tariffs pose to its economy. But United States and Canadian negotiators remain far apart over the potential quotas, with Ottawa insisting on a higher limit and a more flexible system, according to several people briefed on the continuing talks.