The currency concerns are the latest wrinkle in increasingly strained relations between Washington and Beijing. They come as Mr. Trump is considering a meeting with Xi Jinping, China’s president, at the Group of 20 summit meeting in Argentina next month in hopes that the two leaders can defuse the escalating trade war and reach agreement on some sort of trade deal.

“We’re going to make sure currency is definitely part of these discussions,” Mr. Mnuchin said in an interview with CNBC. “We want to make sure that whatever we make up on trade, we don’t lose on currencies.”

He added that he wants a future trade agreement to include a currency provision similar to what was included in the United States-Mexico-Canada Agreement. That deal, which revised the North American Free Trade Agreement, included a commitment by the three countries to avoid manipulating exchange rates and greater transparency in reporting data on international reserve balances.

Mr. Mnuchin acknowledged that trade negotiations with China had taken a step backward in recent months, but insisted that his Chinese counterparts understood what concessions and changes the United States was seeking. Mr. Mnuchin signaled that a meeting with Mr. Trump and Mr. Xi would only take place if there were signs that talks between the two nations were making headway.

“We’ll see if we make progress, if that makes sense,” he said.

For months, American and Chinese officials have been holding back-channel discussions to try to break the trade stalemate. Formal, high-level talks have been scarce, however, as Mr. Trump has moved forward with tariffs on $250 billion of Chinese imports and Chinese leaders have insisted that they will not make a deal under duress. A Chinese delegation canceled a visit to Washington last month after the United States announced more tariffs and Mr. Trump responded by threatening to levy taxes on all Chinese imports.