A slimmed-down deal could also open Mr. Trump up to criticism from Democrats, who in some cases are more aligned with the president’s aggressive approach to pressuring China than many Republicans.

“Anything less than a full effort to secure a fundamental reset of the U.S.-China trade relationship is a betrayal of the American economy and the future of American workers, industry, consumers and innovators,” said Representative Richard Neal of Massachusetts, the Democratic chairman of the House Ways and Means Committee. “The Trump administration needs to stiffen its spine and get tough in these China talks.”

Trump administration officials have been debating whether they can push more tariffs on China without facing significant repercussions. China’s economy is already slowing, in part because of the tariffs, and any further weakening could hurt global economic growth and the United States economy, which is itself showing signs of cooling.

Mr. Mnuchin has been particularly interested in how big a role America’s trade actions are playing in China’s recent economic weakness.

Trump administration officials have debated whether they should follow through with plans to raise tariffs to 25 percent, from 10 percent, on March 2 if China does not maintain the promises Mr. Xi made to Mr. Trump, like accelerating purchases of American goods and making structural changes to its economy.

Progress over the next six weeks could result in an extension of the March 2 deadline, even if a final deal is not reached, or some tariff relief as a reward for initial changes that China says it is willing to make. But the decision will ultimately rest with Mr. Trump.

One question bedeviling the talks is how to enforce any trade agreement with China, given its opaque business environment and largely managed economy. One option that administration officials have considered is “snapback” tariffs, which would be reimposed if China appears to be reneging on its commitments.