In an article posted late Tuesday on the website of China Central Television, the state broadcaster, Mr. Xi said he stressed to Mr. Trump “that the two countries should resolve economic and trade issues through dialogue on even ground, and the key is to accommodate each other’s reasonable concerns. We also hope that the U.S. will treat Chinese companies fairly.”

“I agree that the economic and trade teams of the two countries should maintain communication on how to resolve differences,” Mr. Xi said, according to the article.

It is far from guaranteed that a deal will be reached quickly, if at all. The two sides remain far apart on several issues, including how many of Mr. Trump’s tariffs on roughly $250 billion of Chinese products will come off and whether the trade agreement must be codified in Chinese law.

But both leaders are under economic pressure to come to an agreement. American tariffs have taken a toll on the exports that help power the Chinese economy, raising pressure on Chinese leaders to persuade the Trump administration to come to a truce. Mr. Trump also faces pressure from American lawmakers and businesses, including the manufacturers and retailers who import parts and finished products from abroad, and American farmers and other exporters who have been hurt by retaliatory tariffs from China.

On Tuesday, senators in both parties argued that Mr. Trump’s trade war was inflicting real damage on their constituents, and appealed to Mr. Lighthizer to help soften the blow by ensuring that certain products would be exempt from the president’s 25 percent tariffs.

“Having an exclusion process in place that is usable for these manufacturers who are being harmed, and in some cases harmed greatly, needs to be addressed,” said Senator John Thune of South Dakota, the No. 2 Senate Republican. “There are so many of these unintended consequences, I think, of some of the trade policies that are in place right now.”

The United States has exempted certain products from previous rounds of tariffs, but it is unclear whether any exclusions will be granted if the next $300 billion goes into effect. On Monday, dozens of executives from toymakers, clothing companies, port operators and telecom providers came to Washington to testify in the first of seven days of hearings about how the next round would affect them.