The setback comes at a time when Chinese and American officials appeared to be making progress toward defusing, at least temporarily, a trade war that has been underway for more than a year.

Mr. Trump and his advisers have begun looking for ways to find a compromise with China that would forestall another round of tariffs on Chinese goods that are scheduled for later this year, and perhaps roll back some of the existing tariffs, people with knowledge of the White House’s strategy said. The United States has already placed tariffs on more than $360 billion of Chinese products. It plans to raise tariffs on $250 billion worth of Chinese goods to 30 percent on Oct. 15 and impose more levies in December.

Chinese officials have scaled back their expectations for eliminating American tariffs by quietly dropping earlier public demands that any deal must immediately get rid of all of Mr. Trump’s levies. They have also resumed buying American farm goods as a good-will gesture to help establish a negotiating environment in which an initial deal may be possible.

Still, an agreement is far from guaranteed. Both sides have come close to a deal in the past, including in May, only to have it fall apart at the last moment and tip the countries back into an escalating trade war.

Mr. Trump and his advisers have insisted they are still pushing for a comprehensive deal that would require Beijing to loosen state control over China’s economy. However, they have also discussed scenarios in which they would ease tariffs on roughly a third of the $360 billion worth of Chinese goods penalized so far and delay further tariff increases, in return for concessions on intellectual property, substantial agricultural purchases and other benefits, people familiar with the matter said.

It is far from clear whether either Mr. Trump or Xi Jinping, his Chinese counterpart, would agree to any interim compromise, or that the two sides’ top negotiators could find enough common ground to work toward an initial deal when they meet next week. Even if they do, the broader trade war would continue to rage, leaving in place American tariffs on at least $250 billion in Chinese goods, plus some of Beijing’s retaliatory measures on American farm products and other imports.

But economic and political pressure is growing on both sides to ease the trade war. China’s growth continues to slow, while American farm exports have slumped. Manufacturing in the United States continues to contract as businesses express concern about the uncertainty posed by the trade fight. Farmers and rural voters largely continue to back Mr. Trump, but their support is beginning to waver, and the president is eager to shore up that vote heading into the 2020 campaign.