WASHINGTON — President Trump said on Thursday that China would resume purchases of American farm goods and Beijing confirmed that Chinese companies were making inquiries about buying agricultural products, the latest sign that both sides are trying to ease tensions that have pushed the bilateral relationship to its rockiest point in decades.

The president’s announcement, made on Twitter on Thursday morning, followed a day of cooling trade tensions, in which China announced that it would grant some limited exemptions to its tariffs for American products, and Mr. Trump responded by promising to delay his next tariff increase by two weeks to Oct. 15.

“It is expected that China will be buying large amounts of our agricultural products!” the president said on Twitter on Thursday.

China’s Ministry of Commerce said some Chinese companies were beginning to make inquiries about resuming purchases of American agricultural products. “Soybeans and pork are all within the scope of inquiry,” said Gao Feng, a spokesman for the ministry. “I hope that China and the United States will move in the same direction and create favorable conditions for consultations.”

American and Chinese negotiators now plan to meet in person in early October, before Mr. Trump’s deadline to increase tariffs on $250 billion worth of goods to 30 percent from 25 percent. Expectations for quickly resolving the significant differences between the two sides remain modest. But the recent de-escalation increases the likelihood that the next round of tariffs might be averted, perhaps eventually opening a path to an agreement that would smooth relations between the countries.

Markets, which have gyrated with every twist and turn in the trade war, rose on the potential that the two sides could de-escalate a trade war that has gone on far longer than most investors had expected. The S&P 500 index rose 0.45 percent by noon, while the Dow Jones industrial average gained 0.42 percent.

Mr. Trump’s tariff threats against China have weighed heavily on markets, as the trade war’s effect on the economy has become more obvious in recent months. A manufacturing index published this month showed American factory activity contracting for the first time in three years, while an index of consumer sentiment reflected the biggest decline since 2012, where one in three consumers spontaneously mentioned tariffs.

The signs of easing follow a familiar pattern for Mr. Trump, who has routinely vacillated between punishing China and trying to cool tensions when markets and economic data start to wobble.

Relations between the countries have worsened since May, when China backed away from a nearly complete deal that would have required it to codify the agreement into Chinese law, which Beijing said would infringe on its sovereignty. Since then, Mr. Trump has placed tariffs on an additional $112 billion of Chinese products and threatened further tariff increases in October and December.

China has responded to the escalation by increasing tariffs on $75 billion of American goods. Chinese state-owned companies have also suspended their purchases of American soybeans, pork and other products, a severe hit to American farmers who have already lost markets because of the trade clash.

Mr. Trump and his advisers have weighed whether striking a deal with China would be a boon or liability to the president heading into his re-election. They have been working for months to secure a trade deal that is strong enough to dodge criticism from both Democrats and Republicans that Mr. Trump is folding to America’s biggest economic competitor.

The details of the trade agreement the United States is discussing with China are tightly held. But they have revolved around China strengthening its protections for American intellectual property, opening up its markets to competition from American firms and making large purchases of American products, like natural gas and soybeans.

The Trump administration has also pressed China to make more structural changes, for example rolling back the influence of state-owned enterprises in its economy. But China has balked at making any concessions it sees as compromising its ability to manage its economy, or signing a deal it perceives as uneven. For their part, the Chinese have demanded the rollback of the tariffs Mr. Trump has placed on $360 billion of Chinese products, as well as leniency for Huawei, the Chinese telecom giant the United States has cut off from purchasing American supplies.

Mr. Trump’s closest advisers said the delay in tariffs would pave the way for smoother relations.

Treasury Secretary Steven Mnuchin said on Thursday that Mr. Trump was making a “good gesture” by agreeing to move the deadline by two weeks so that it did not conflict with China’s celebration on Oct. 1 of its founding 70 years ago.

“The president delayed it because of a request from the vice premier,” Mr. Mnuchin said on CNBC. “The optics of us raising the tariffs on Oct. 1, which is their 70th anniversary, caused them grave concern on the symbolism.”

Mr. Mnuchin would not comment on the whether the United States and China are discussing an agreement that is smaller in scope than they originally hoped. But asked about thorny issues, he made clear that the unrest in Hong Kong would not be part of the trade talks.

“Hong Kong is definitely not on the table,” he said. “That’s an issue for the secretary of state to deal with. That’s not a trade issue.”

Mr. Mnuchin did not address whether Huawei would be discussed. He said the critical issues in the negotiations remained the protection of American intellectual property, an end to China forcing American companies into joint ventures, currency manipulation and increased purchases of American agricultural products.

“We expect and we want them to buy agriculture,” he said. “We view that as a personal attack on our farmers.”

Some White House officials played down the significance of Mr. Trump’s reprieve on Thursday.

“It’s a small thing in the scheme of things,” Peter Navarro, Mr. Trump’s trade adviser, said on CNN, noting that the delay was for only two weeks. “The Chinese are paying the tariffs anyway.”

Mr. Navarro accused the Chinese of economic aggression and stealing American intellectual property. He also pushed back against Republican lawmakers, such as Senator Patrick J. Toomey of Pennsylvania, who have been voicing their frustration about the tariffs.

“He’s waving the white flag, not the American flag,” Mr. Navarro said of Mr. Toomey.

Mr. Navarro also seemed skeptical that China would actually step up its purchases of American agricultural products.

“Let’s see if the Chinese fulfill their commitments,” he said. “The problem we’ve always had with the Chinese is that they don’t necessarily honor their commitments.”

Business leaders are hoping for a quick resolution to the trade fight.

Jennifer Safavian, the executive vice president of government affairs at the Retail Industry Leaders Association, which represents companies including Walmart, Best Buy and Target, said they were hopeful that the delay in American tariffs would lead to productive talks.

“A resolution is sorely needed that puts an end to the tariff increases,” Ms. Safavian said. “Negotiating a path forward that puts an end to the erratic tariff increases and provides some dose of certainty to businesses should be the goal for the October trade discussions.”

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