On Monday, the White House said that Robert Lighthizer, the United States trade representative who is a longtime China skeptic, would lead the talks with Beijing. The choice of Mr. Lighthizer, who has a reputation as a tough negotiator, conveyed a tough road ahead.

The days since the agreement have also been marked by confusion over the timetable to reach a deal. The White House said on Monday that the two sides had until March 1 to reach an agreement but Mr. Trump suggested in one of his tweets that the deadline could be extended.

The lack of clarity has not pleased investors, who were briefly relieved after initial reports of a trade truce. Stocks fell sharply on Tuesday, including those in the industrial sector, which is widely exposed to risks related to the trade fight between Washington and Beijing. Shares in Boeing and Caterpillar, companies with significant sales in China, tumbled.

Members of Mr. Trump’s economic team continued to temper optimism about a deal on Tuesday.

Mr. Mnuchin said that China had agreed to buy $1.2 trillion of American products, but he could not offer specifics on what would be bought and when.

“They have said that these are targets and that that is their expectation,” Mr. Mnuchin told the Fox Business Network. “And that in the short term there would be some very specific commitments.”

Mr. Kudlow was careful to downplay suggestions that the Trump administration was really seeking a full overhaul of America’s trade relationship with China through the talks.

“I don’t think these trade talks are designed to completely change the system,” said Mr. Kudlow, who also spoke at the WSJ CEO Council event. “These talks are centered on a variety of specific issues.”