By MARK LANDLER, GLENN THRUSH and KEITH BRADSHER, New York Times–

President Trump is projecting a steely facade as he prepares for a critical meeting on trade this weekend with President Xi Jinping of China. But behind his tough talk and threats of higher tariffs is a creeping anxiety about the costs of a prolonged trade war on the financial markets and the broader economy.

That could set the stage for a truce between the United States and China, several American officials said, in the form of an agreement that would delay new tariffs for several months while the world’s two largest economies try to work out the issues dividing them.

Such an outcome is not certain. Administration officials have expressed deep disappointment with China’s response to Mr. Trump’s pressure so far, characterizing it as a list of proposals, transmitted in Chinese, which they say would do little to curb China’s theft of American technology or address its other predatory trade practices.

But Mr. Trump has signaled a new willingness to make a deal with Mr. Xi, a leader he has treated solicitously and will meet over dinner on Saturday in Buenos Aires, after a summit meeting of leaders of the Group of 20 industrialized nations.

The gyrations in the stock market, the rise in interest rates and thousands of layoffs announced by General Motors this week have all rattled Mr. Trump, officials said, fueling his desire to emerge from his meal with Mr. Xi with something he can claim as a victory.

“There’s a good possibility that we can make a deal, and he is open to it,” Mr. Trump’s chief economic adviser, Larry Kudlow, said Tuesday. But if the meeting failed to produce a breakthrough, he said, Mr. Trump was “perfectly happy to stand on his tariff policies.”

At the moment, the administration plans to raise existing tariffs on $250 billion worth of Chinese goods, to 25 percent from 10 percent, on Jan. 1. Mr. Trump has also threatened to impose tariffs on an additional $267 billion of Chinese goods — a step many fear would plunge the two giants into a full-fledged economic Cold War.

If the two leaders agree to talks, however, officials said Mr. Trump would most likely postpone the increase to 25 percent and hold off on any new tariffs. That would be similar to a deal he struck last July with the European Union, in which he agreed to delay auto tariffs in return for a pledge by Europe to buy American soybeans and natural gas.

The divisions inside the West Wing over trade remain fierce, as they have since the beginning of Mr. Trump’s presidency, and the contest for Mr. Trump’s ear will most likely continue until the moment he sits down with Mr. Xi in Argentina.

More mainstream advisers like Mr. Kudlow and the Treasury secretary, Steven Mnuchin, are urging him to compromise, while hard-liners like Peter Navarro, the director of the White House trade office, argue that he should keep ramping up the pressure on China until it folds.

Mr. Navarro, a favorite of Mr. Trump’s, had initially been excluded from the trip to Argentina, which led some to conclude that the hard-liners had lost ground. Mr. Trump also sided against Mr. Navarro after Mr. Kudlow took a shot at him on television. But the United States trade representative, Robert Lighthizer, has since authorized Mr. Navarro’s travel, raising the prospect that he will be on hand to encourage Mr. Trump to play hardball.

For Mr. Lighthizer, a veteran trade lawyer who has sued China for flooding the American market with cheap steel, the negotiations present an opportunity to drive a hard bargain.

But he also sees the meeting between Mr. Trump and Mr. Xi as a potential danger, especially if Mr. Trump opts for a quick handshake deal that would delay or scrap the new tariffs in hopes of buoying jittery markets, according to people familiar with his thinking.

Mr. Lighthizer also faces a challenge from Mr. Mnuchin, who has made it clear that he views himself as the nation’s chief negotiator, according to administration officials. Mr. Navarro, people who know him say, regards Mr. Mnuchin as one of the circle of “globalists” pressuring Mr. Trump to abandon his promise to crack down on China.

Another American official said the major internal debate now was over the scope of a compromise Mr. Trump could offer Mr. Xi: postponing the increase in tariffs to 25 percent, plus the $267 billion in new tariffs — or only the new tariffs.

That underscores how much Mr. Trump’s position has changed from a few months ago, when he announced sweeping tariffs on China, asserted the Chinese were not yet ready to negotiate an agreement and declared that trade wars were “easy to win.” Only two weeks ago, disagreements between China and the United States over trade scuttled attempts to produce a joint communiqué after an Asian economic meeting.

Mr. Trump is acutely aware of the threat an economic downturn poses to the foundation of his presidency. That has made him receptive to the counsel of moderates like Mr. Mnuchin and Mr. Kudlow, as well as outsiders like the Wall Street financier Stephen A. Schwarzman who have been warning him he will be blamed for job losses, market losses and other economic damage from a prolonged trade war with China.

On Tuesday, Mr. Kudlow deflected questions about the depressing effect of trade tensions on the markets. He argued that the tariffs affected only a fraction of the American economy, which is still showing robust growth in jobs and incomes. And he said the negative effect had been much greater in China.

“I’m not suggesting that there aren’t winners and losers in that game,” Mr. Kudlow said. “But on the other hand, I think we are in far better shape to weather this than the Chinese are.”

In China, where growth is slowing and the stock market has swooned, the government is mulling a broad cut in import tariffs that would lower trade barriers for companies around the world, including those in the United States, people briefed on Beijing’s thinking said.

But the American demands could be a major sticking point. Chinese leaders are reluctant to accept any permanent American tariffs on Chinese goods, fearing that such a compromise would be seen at home as a sign of weakness.

Until now, the two sides have been mostly talking past each other. Chinese officials have expressed puzzlement to visiting Americans about why the administration has not responded to the 142-point list of proposals they sent to the United States. Mr. Kudlow said that once his colleagues translated it into English, they discovered there was little new there.

“We can’t find much change in their approach,” he said. “What’s the timetable? What’s the enforcement mechanism?”

For all the turbulence, Mr. Lighthizer is resolved to make the best of the situation, according to people who have spoken to him in recent days. That is in part because Mr. Trump is still pleased he was able to secure a new North American Free Trade Agreement deal before the summit meeting.

But even that deal has hit a pothole. Prime Minister Justin Trudeau of Canada remains in a standoff with Mr. Trump over Canada’s demand that the United States remove steel and aluminum tariffs as part of the new treaty.

Mr. Trudeau has yet to confirm to American officials that he will attend the ceremonial signing of the agreement in Buenos Aires with Mr. Trump and Enrique Peña Nieto, the outgoing president of Mexico. Mr. Trudeau could end up delegating that task to a subordinate, according to two people with knowledge of the situation, a snub that could aggravate tensions with Mr. Trump.

Mr. Trump will also have to mollify another bruised ally, Britain, after he told reporters on Monday that the departure agreement Prime Minister Theresa May negotiated with the European Union might bar Britain from trading with the United States. Mr. Kudlow said Mr. Trump was referring to a provision in the deal that he said could prohibit Britain from negotiating a separate free-trade agreement with the United States.

British officials said there was nothing in the agreement that prohibits Britain from negotiating a bilateral trade deal with the United States — or anybody else. They expressed bafflement that Mr. Trump, an avowed supporter of Brexit, would seek to sabotage the most realistic path of negotiating Britain’s departure.

Mr. Trump’s outburst on Brexit underscored his unpredictability — the same quality he will take into his meeting with Mr. Xi. Chinese and American officials both recognize the value he places on grand bargains, reached after direct leader-to-leader negotiations.

Aside from the dinner, Mr. Kudlow said there were no plans for any other meetings between Chinese and American officials. But Mr. Trump’s aides have tried, in different ways, to prepare the ground for the meeting with Mr. Xi.

Mr. Mnuchin, who has generally been loath to challenge Mr. Trump directly, views the negotiations with China as critical and sees the fallout from the trade war as a threat to his legacy, according to a person familiar with his thinking.

At times, several officials said, the Chinese have sought to avoid Mr. Lighthizer in favor of Mr. Mnuchin, who communicates regularly with Mr. Xi’s top trade official, Liu He. While Mr. Mnuchin shares Mr. Lighthizer’s view that the tariffs are driving China to the bargaining table, he has told Mr. Trump that he thinks the time has come to reduce exposure to the “volatility” of markets reacting to the tensions, according to several officials.