The trade deal will exclude South Korea from the steel tariffs, in exchange for that country capping its exports to the United States at 70 percent of the average of its export levels from 2015 through 2017. Korea will still face the aluminum tariffs.

The revised agreement also lacks the robust “side deal” on currency manipulation that administration officials said would be included to prevent South Korea from weakening its currency, the won. Currency devaluation, as it is called, has been of particular concern to Mr. Trump, who has accused other trading partners, like China and the European Union, of trying to weaken their currencies so that Americans using the United States dollar can buy more of their products.

“We’re going to be able to defend ourselves against currency undervaluations because, as part of this deal, there’s a very nice side deal agreement that the secretary of Treasury is negotiating over currency undervaluation,” Peter Navarro, a top trade adviser, told NPR in March. Mr. Navarro added that the currency agreement is “a benchmark for what we’ll be doing going forward.”

That side deal has yet to materialize. In August, the United States trade representative published the “agreed outcomes” from its negotiations with the Koreans: 24 pages of technical language and correspondence between officials from both countries, including agreements on American auto and prescription drug exports and Korean textile exports. There is no mention of currency in the agreement, or of any pending side deal.

In a fact sheet released Monday afternoon by the White House, Trump administration officials said that “outside” the Korea pact, “the Treasury Department has an understanding with South Korea to avoid competitive devaluation and practices that provide an unfair competitive advantage. The understanding includes strong commitments on exchange rate practices, robust transparency, and reporting.”

Mr. Navarro did not immediately respond to questions on Monday about what that “understanding” comprises, and whether it is in writing.

Asked about the lack of a side deal this month, Treasury officials did not respond directly to questions whether it exists or will exist, saying instead that they are happy with the state of talks with the Koreans over currency.