When President Biden meets President Xi Jinping of China at a lush estate on the edge of Silicon Valley on Wednesday, his primary goal will be simple: find a way to avoid an increasingly bitter competition with China from tipping into conflict.

For two leaders who have agreed on very little as their nations have spiraled into their worst relationship in four decades, there have been hints of how they will try to nudge toward the appearance of agreement. A senior administration official said they are expected to reach the outline of an agreement that would commit Beijing to regulating components of fentanyl, the drug that has driven a devastating opioid epidemic in the United States. But China has made similar commitments before.

They are likely to announce a new forum for a discussion of how to keep artificial intelligence programs away from nuclear command and control — at the same moment the United States is denying China the advanced chips it needs to develop and train A.I. programs. And they will probably discuss resuming military-to-military communications, which China cut off after Nancy Pelosi visited Taiwan last year, when she was speaker of the House. But there have been periods of military-to-military contact since the George W. Bush administration.

The interactions between the two leaders when they meet at the lush Filoli estate, a historic house and garden just northwest of the Stanford campus, have been carefully choreographed. Senior Chinese officials have discussed them in meetings with Mr. Biden’s most trusted aides, including Jake Sullivan, the national security adviser, and Antony J. Blinken, the secretary of state.

But plenty of thorny issues remain to complicate the discussions, including some Mr. Biden’s aides have said he intends to raise, such as the wars in Ukraine and Gaza and the upcoming election in Taiwan, a self-governing island that China claims as its own.

In briefing after briefing, administration officials have tried to lower expectations about the kind of concrete commitments that used to surround such summits, saying that the mere fact that the leaders of the world’s top two economies, and most potent militaries, are communicating again is itself a sign of progress.

Graham Allison, a Harvard professor and the author of a book asking whether the two countries are destined for war, wrote in The National Interest that the meeting would encapsulate what he called “two contradictory but nonetheless inescapable facts.”

“First, the U.S. and China will be the fiercest rivals history has ever seen,” he wrote. “Second, each nation’s very survival requires a degree of cooperation from the other.”

Mr. Biden arrived in San Francisco on Tuesday afternoon with the city locked down for the summit for Asia-Pacific Economic Cooperation, known as APEC, a group of 21 countries that surround the Pacific Ocean. (He dispatched Treasury Secretary Janet L. Yellen to meet Mr. Xi when he landed in San Francisco on Tuesday evening.)

Mr. Biden’s only public event on Tuesday was a fund-raiser alongside Vice President Kamala Harris, during which he suggested that economic headwinds in China, along with the Biden administration’s work to build a network of partners in the Indo-Pacific to counter Chinese ambition, had brought Mr. Xi to the negotiating table.

“President Xi is another example of how re-establishing American leadership in the world is taking hold,” Mr. Biden told the crowd. “They’ve got real problems, folks.”

It was hardly the first time that Mr. Biden has referred to China’s economic slowdown, and it was only five months ago that he referred to him as a “dictator,” a comment that his advisers quickly tried to back up.

No joint statement will be coming on Wednesday to try to smooth over such tough talk. American officials say each government will provide its own account of the discussions.

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