Mr. Trump has sought to leverage trade and North Korea with China for months, initially expressing optimism after hosting Mr. Xi at his Mar-a-Lago estate in Florida, only to later grow discouraged that Beijing was not following through. The effort has now reached a decisive point with the overt threats of American military action against North Korea — warnings clearly meant for Beijing’s ears.

China is widely seen as critical to any resolution to the nuclear crisis because of its outsize role as North Korea’s main economic benefactor. China accounts for as much as 90 percent of North Korea’s total trade and supplies most of its food and energy while serving as the primary purchaser of its minerals, seafood and garments.

But even though the effectiveness of the new United Nations sanctions depends largely on China’s willingness to enforce them, the Trump administration so far has failed to come up with enough incentives to compel China to do so, analysts said.

In their phone conversation on Friday night, Mr. Xi stressed that it was “very important” for the two leaders to maintain contact to find “an appropriate solution to the nuclear issue on the Korean Peninsula,” according to a statement carried in the Chinese state-run media. The language indicated China wants to push forward with a diplomatic proposal for North Korea that the Trump administration has brushed aside.

The Chinese statement urged the “relevant sides” — a reference to North Korea and the United States — to “avoid words and actions that exacerbate tensions.” It did not explicitly criticize North Korea, which issued its own searing rhetoric all week, including a threat against Guam, and did not draw a clear distinction between Washington and Pyongyang.

In its own account of the call, the White House emphasized points of concurrence. “President Trump and President Xi agreed North Korea must stop its provocative and escalatory behavior,” read a statement from the White House issued early Saturday morning. “The presidents also reiterated their mutual commitment to denuclearization of the Korean Peninsula.”

If Mr. Trump was trying to move Mr. Xi toward bolder action against the north, he did so while the Chinese leader is preoccupied with his own domestic political machinations, attending to a once-every-five-year political shake-up in the top ranks of the Communist Party.

Mr. Xi is believed to be at the beach resort at Beidaihe on the coast east of Beijing, where the leadership conducts a secretive retreat every summer, sometimes emerging casually dressed in open neck shirts and Windbreakers for photographs on the strip of sand along the beachfront.

The final stages of the political process to win Mr. Xi’s favor for a place on the standing committee of the party, now a seven-member body that makes the final decisions on the nation’s affairs, is underway among the resort’s villas and hotels, China’s political analysts said.

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The selection will be unveiled at a national congress in Beijing sometime between September and November. Until then, almost all other matters, including foreign policy, are put on hold, the analysts said.

Still, the leadership has been vexed that the Trump administration has paid scant attention to China’s proposal for a “freeze for freeze” solution to North Korea. Described many times by China’s foreign minister, Wang Yi, the notion calls for North Korea to freeze its nuclear weapons and ballistic missile program at current levels in exchange for the United States drawing down military exercises off the Korean Peninsula.

So far, the United States has dismissed the proposal as a nonstarter. Instead, to China’s irritation, the United States is looking to increase missile defenses in South Korea. In some respects, though, Secretary of State Rex W. Tillerson has tried to please Beijing by pledging that Washington does not seek to overthrow the North Korean leader, and does not plan to send American troops north of the 38th parallel that divides North and South Korea.

Mr. Xi is said to be exasperated with Kim Jong-un, a leader much his junior, whom he openly disparaged during his meetings in Florida in April with Mr. Trump, American officials say. But despite the frustration with Mr. Kim, China still prefers to have what it considers a relatively stable North Korea under Mr. Kim rather than a collapsed state that could result in a united Korean Peninsula on its border, with American troops in control.

In rebuffing the “freeze for freeze” proposal, Washington has raised suspicions in Beijing about its true intentions, said Yun Sun, a China expert at the Stimson Center in Washington. Chinese leaders believe the United States sees its true rival as China, a mammoth economy, and not North Korea, one of the poorest countries on earth, Ms. Sun said. In this estimation, Washington is merely using North Korea to mount a military containment strategy around China, she said.

“The Chinese operate from the conviction that China remains and will always be the No. 1 strategic threat to the U.S., so the issue of North Korea will be used against China — through sanctions, provocations and everything else,” she said. China was also annoyed, Ms. Sun said, that the United States refuses to discuss a “grand bargain” or “end game” on the future of the Korean Peninsula. Of most interest to China, she said, is the future disposition of American forces in South Korea, now standing at 28,500 troops.

The phone conversation between Mr. Trump and Mr. Xi will be followed by a visit from the chairman of the Joint Chiefs of Staff, Gen. Joseph F. Dunford Jr., who is expected in Beijing on Monday. General Dunford will also visit South Korea and Japan.

The general’s visit, planned earlier this summer, is the first by a senior American official to Beijing since Mr. Tillerson met with Mr. Xi in March.

Much of the diplomacy between China and the United States has been conducted between Mr. Trump’s son-in-law, Jared Kushner, and the Chinese ambassador in Washington, Cui Tiankai. Those talks have concentrated on Mr. Cui’s efforts to stave off punishing trade tariffs against China that are gathering momentum in White House discussions.

During his two-day visit, General Dunford is likely to use the opportunity to drive home arguments for the Chinese to put more pressure on the Kim government, said Brian McKeon, who was a senior Pentagon official in the Obama administration.

A major point of dispute will likely be American plans to deploy more missile defenses in South Korea, he said. China vehemently opposes the Terminal High Altitude Area Defense system, or Thaad, that has already been deployed in South Korea, calling it a threat to its own security.

“I would expect that Dunford will make the usual request that they put more pressure on the regime to behave, and to recognize that Kim’s actions threatens our core interests, which means we will have to continue to take measures that Beijing doesn’t like, for example the deployment of Thaad,” Mr. McKeon said.

Jane Perlez reported from Beijing, and Peter Baker from Bridgewater, N.J. Eric Schmitt contributed reporting from Washington.

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