On Thursday, three powerful Senate Democrats, including Chuck Schumer of New York, sent a letter to Mr. Trump, warning that any first-phase deal that did not include meaningful changes to the way China structured its economy would be “a severe and unacceptable loss for the American people.”

Some mocked the president for solving a crisis of his own making.

“China Phase-1 deal is the equivalent of a gunman, who had taken hostages, surrendering to authorities, with no one killed, but his manifesto never published,” Jorge Guajardo, the former Mexican ambassador to China, tweeted. “No harm done to anyone, back to normalcy, madman contained, but the shopping mall lost a lot a customers during standoff.”

For a year and a half, Mr. Trump has alternated between praising China and ratcheting up tariffs on the country as he tried to press Beijing for trade concessions. In October, Mr. Trump announced that the United States and China had reached an agreement in principle on the first phase of a trade deal. But in the weeks since, a concrete agreement proved elusive as the two countries grappled over its precise terms.

Chinese negotiators pushed their American counterparts to remove as many of the existing tariffs as possible, while the Trump administration pressed China to make more purchases of soybeans, poultry and other goods to help relieve the pressure the trade war had put on American farmers. Mr. Trump also wants China to buy more American products to help narrow the trade gap between what the United States sells to China and what it imports.

To ensure that China keeps its commitments, the Trump administration has insisted on periodic reviews, as well as an agreement that China’s agricultural purchases would not drop below a certain amount. If China violates the terms of the agreement, tariffs that the Trump administration had removed would snap back into place.

China has been willing to discuss purchases of American agriculture, especially since a disease has devastated its swine population and led to spiraling pork prices. But in previous discussions, Chinese negotiators had pushed back against promising set purchase amounts far into the future, saying such an arrangement could anger its trading partners and violate its commitment to the World Trade Organization to treat all members equally.