Robert E. Lighthizer, the chief U.S. trade negotiator, and Treasury Secretary Steven Mnuchin “met with President Trump to discuss the ongoing trade negotiations with China. The Ambassador and Secretary then had a working dinner with Vice Premier Liu He, and agreed to continue discussions,” the White House said in a statement.

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In Beijing, the Commerce Ministry said China “deeply regrets” the decision to increase the tariffs and “will have to take necessary countermeasures.”

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“We hope that the U.S. and China will meet each other halfway and make joint efforts to solve the existing problems through cooperation and consultation,” a spokesman said in a statement.

Chinese stock markets, after suffering big losses earlier in the week, actually gained on Friday. The Shanghai Composite Index rose 3.1 percent and the Shenzhen Component Index gained 4 percent.

Because the higher tariffs apply only to goods that leave China on Friday — not shipments already approaching American shores — officials still have time to work out a last-minute solution.

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But no matter what happens at the bargaining table, relations between the world’s two largest economies, accounting for roughly 40 percent of global output, appear certain to change.

“They’re really determined to go in a different direction,” said Timothy Stratford, chairman of the American Chamber of Commerce in China and a former U.S. diplomat in Beijing. “The U.S. is recalibrating its policy toward China.”

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At stake — along with industrial supply chains supporting millions of American jobs — was the president’s core campaign promise to rebalance the U.S. trading relationship with China in favor of American blue-collar workers. Nearly $660 billion in goods were traded between the two countries last year.

U.S. officials said Trump’s “America First” stance rocked Chinese leaders and halted the erosion of American manufacturing and technology industries by Chinese trade practices.

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But the tariff war, which has lasted more than a year, also has claimed numerous casualties. The Dow Jones industrial average is below its level on Jan. 22, 2018, when Trump began the dispute by imposing levies on imported washing machines. The benchmark index fell nearly 450 points Thursday before closing down 139 points, or 0.5 percent.

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As China retaliated for subsequent tariff salvos, American farmers and major U.S. industries were caught in the crossfire.

China is the second-largest export market for U.S.-built vehicles. But Chinese customers, who bought roughly 260,000 vehicles from the United States in 2017, bought more than 100,000 fewer last year, according to John Bozzella, president of Global Automakers, an industry group.

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“What was the difference? The difference was the [Chinese] tariffs went from 15 to 40 percent,” Bozzella said. “So that’s what’s at stake.”

The politics of 2020 are also an inescapable subplot to the trade drama. In recent days, Trump, writing on Twitter, linked Chinese backsliding on a tentative agreement to Beijing’s desire to wait to make an easier deal with a Democratic president “and thereby continue to ripoff the United States.”

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Democratic leaders have publicly supported the president’s hard line. Those statements illustrate the evident bipartisan consensus favoring a tougher stance toward Beijing — but also the political risks for the president of making a deal that a 2020 rival might criticize as soft.

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“President Trump has successfully identified Chinese economic behavior that has seriously harmed our economy over time. If U.S.-China talks eventually produce a weak deal, his chances of reelection drop no matter who the Democratic candidate is,” said Derek Scissors, a China expert at the American Enterprise Institute. “If the president does what he insists he will — get a great deal or walk — it will not only boost his reelection prospects, it will boost our economy for years to come.”

Trump said Thursday that he had received “a beautiful letter” from Chinese President Xi Jinping and may speak to him by phone, though he did not say whether that would occur before the scheduled increase in tariffs takes effect.

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Trump said Xi’s message was: “Let’s work together. Let’s see if we can get something done.”

Lighthizer began meeting shortly after 5 p.m. Thursday with Liu to continue negotiations aimed at a comprehensive deal.

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Those talks had been proceeding smoothly, with U.S. officials predicting a final accord could be agreed to as soon as this week.

But China last weekend angered the president by trying to water down its commitments, according to Lighthizer. Chinese officials balked at specifying in the agreement which laws would be amended to address U.S. concerns over forced technology transfer and intellectual property protection, U.S. officials said.

“We were getting very close to a deal, and then they started to renegotiate the deal. We can’t have that,” the president said, following a White House event on preventing surprise medical bills. “It was their idea to come back.”

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Liu, speaking upon his arrival in D.C., acknowledged the recent difficulties. “Much to our regret, we had some problems during our negotiation,” he told Xinhua and CCTV. But, he said, “China believes that raising tariffs is not a solution to the problems.”

Trump said that he expected “a very strong day” at the negotiating table but added that “our alternative is an excellent one,” an apparent reference to the tariff increase.

China had vowed to retaliate “in kind” if the president proceeds with the increase to 25 percent from 10 percent on $200 billion in Chinese products.

Along with Friday’s increase, the president has also threatened to extend tariffs to all $540 billion in annual Chinese imports.

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The president had delayed the tariff increase on two earlier occasions in an effort to give negotiators time to strike a bargain that would include massive purchases of American products and structural changes in China’s state-led economy.

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After more than five months of accelerated diplomacy, following a Trump-Xi dinner in December at the Group of 20 summit in Buenos Aires, several core issues remain to be resolved.

Chinese negotiators insist that all the tariffs the United States imposed last year be eliminated in any deal.

But the president wants to keep some or all of the import taxes in place as leverage to encourage Chinese compliance. The administration is wary of repeating what it sees as the mistakes of earlier Republican and Democratic administrations: reaching agreements with China that lacked ironclad enforcement mechanisms.

Those tariffs are being paid by U.S. importers and, ultimately, by consumers. Yet the president frequently boasts about the revenue the federal government receives from higher tariffs.

Though most economists say such a broadening of the trade conflict would inflict serious damage on both economies, the president insists his tariffs helped the U.S. economy grow at a 3.2 percent annual rate in the first quarter.

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“I’m different than a lot of people. . . . I happen to think that tariffs for our country are very valuable,” Trump said.

Many business leaders, who support the president’s efforts to combat Chinese trade practices, are growing weary of the costs of his preferred tool. Tariffs will cost Polaris Industries Inc. — a Medina, Minn., maker of snowmobiles and motorcycles — roughly $200 million annually if the increase to 25 percent takes effect, said Scott Wine, the company’s chief executive.

“We barely make $400 million profit,” Wine said. “It’s a significant issue.”

The company has 9,000 employees in the U.S. But its main competitor assembles its vehicles in Mexico, escaping the U.S. tariffs on Chinese goods that hit Polaris’s imported wire harnesses and machined parts, he said.

“We’re losing market share right now,” said Wine, who added he would be forced to consider shifting production to Mexico if the tariffs become permanent.

Chinese retaliation could take the trans-Pacific relationship into potentially dangerous territory, according to Chris Krueger, an analyst with Cowen’s Washington Research Group.

During the past year of tit-for-tat tariff exchanges, China has imposed tariffs on all but $10 billion of its purchases from the United States.

To keep pace with Trump’s planned escalation, Beijing may use other weapons, including state-backed boycotts of American products, tighter customs inspections and intensified tax audits of U.S. companies, Krueger said.

The economic and political fallout from such steps “are a lot harder to predict and prone to accident,” he added.