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“We have a one time shot at making a great deal for both countries,” Mr. Trump said, adding, “I would say that it’s more likely that a deal will happen.”

Mr. Trump’s advisers were more cautious, with Robert Lighthizer, Mr. Trump’s top trade negotiator, warning that the United States and China still have “very big hurdles” to overcome. Wilbur Ross, the commerce secretary, said it was “a little early for champagne.”

While significant obstacles persist, the two sides agreed to extend negotiations by 48 hours, and American officials said both had reached what Mr. Trump termed a “final agreement” to stabilize China’s currency, though the specifics of the agreement were not immediately clear.

The United States has been concerned that China could mitigate the effect of tariffs by weakening its currency, which would make Chinese products cheaper to purchase. Some international finance experts found the idea of such an agreement ironic, as the United States for years urged China to allow its currency to float more freely.

Tony Sayegh, a Treasury Department spokesman, did not respond to a request for comment on details of the currency deal.

The Chinese delegation also presented Mr. Trump with a letter from Mr. Xi, as it did last month, which called on both sides to continue their efforts to reach a deal that benefits both countries. Liu He, who has been appointed Mr. Xi’s special envoy and is leading negotiations, concurred that he believed a deal was likely.

Mr. Trump, who has focused for years on how unfair competition from China has hollowed out American manufacturing, has set the bar for his signature trade deal extremely high. His advisers have pressured China to reduce the subsidies that are powering its high-tech industries and to loosen the state’s grip on its economy — moves that would run counter to Mr. Xi’s desire to strengthen China and his control of it.