Mr. Lighthizer, who recently brokered the new North American trade deal, is a longtime critic of China’s trade practices and has repeatedly cautioned Mr. Trump not to accept vague promises that fail to materialize. He will be taking the reins from Mr. Mnuchin, who led previous rounds of negotiations with the Chinese but could not close a deal that satisfied the president.

That choice could rattle the Chinese, who have cozied up to Mr. Mnuchin, viewing him as more moderate.

“The greatest amount of expertise in the administration, on trade and China, is held by Bob Lighthizer,” said Michael Pillsbury, a China scholar at the Hudson Institute who has been advising the Trump administration, adding that the Chinese have been avoiding Mr. Lighthizer out of fear. “The Chinese are wary because they know he’s the real deal.”

Mr. Trump and Mr. Xi agreed during the Group of 20 meeting in Buenos Aires to pause the trade war between the world’s two largest economies for 90 days and work to address several areas of tension, including the trade gap between what the United States imports from China and what it sells to the Chinese. Mr. Trump, who has hit China with tariffs on $250 billion worth of goods, agreed over the weekend to hold off on plans to raise all the tariffs to 25 percent on Jan. 1 and to impose additional levies on all Chinese imports.

On Monday, the president trumpeted what he has called “an incredible deal” for farmers and manufacturers, saying they would be first in line to reap the benefits of his agreement.