Mr. Trump’s public effusiveness is barely reciprocated in China. The state-run media accords Mr. Trump polite coverage, much more so than it did President Barack Obama — a signal that the government, for the time being, would like the Chinese people to view the American president in a positive light.
Among foreign policy experts, however, there is skepticism that Mr. Trump’s flattery of Mr. Xi, and his reliance on the Chinese leader to bear down on North Korea over its nuclear program, will bring the results he wants.
Mr. Trump has said he would give Mr. Xi more on a trade deal if China — North Korea’s main trading partner and sole major ally — cracked down on its recalcitrant neighbor. “I think that, frankly, North Korea is maybe more important than trade,” Mr. Trump said last weekend.
In essence, the Trump administration is asking China to apply maximum economic pressure on the North Korean leader, Kim Jong-un, so that he will relinquish his nuclear arsenal, or at least agree to negotiate on Washington’s terms.
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Analysts say Mr. Xi is likely to take steps to curb the activities of some Chinese companies that help North Korea with the foreign exchange it badly needs, but not all of them. They say he may even, at some point, shut down the oil supply from China that keeps the economy afloat — but if so, only for a short period.
Some analysts said Mr. Trump’s own predictability should not be taken for granted.
“He needs China to help implement what he wants on North Korea,” said Yan Xuetong, director of the Institute for International Relations at Tsinghua University. “It won’t work. Trump will change his attitude to China very soon. I don’t think he will be so nice to our president for very long. His policy toward China is not durable.”
Others noted that it would be against China’s national security interests to side with the United States against North Korea.
“I think this ends unhappily,” said Douglas H. Paal, vice president for studies at the Carnegie Endowment for International Peace. “In the end, China is not going to deliver North Korea on our doorstep. China will say: ‘We’ve done these things. What are you so upset about?’”
Mr. Trump, who likes to do business by phone, is acquiring a reputation for pestering Mr. Xi. He called the Chinese president four days after their summit meeting in Florida last month, saying afterward on Twitter that he had had “a very good call” with Mr. Xi about the “menace of North Korea.”
He called again on April 23. Mr. Paal said he was told by Chinese officials that after that call, Mr. Xi did not appreciate being treated like a midlevel official. Mr. Trump should realize that the Chinese president sets the framework for policies but cannot be expected to keep a checklist of tasks, the officials told him.
Still, Mr. Trump’s impulse to reach out to Mr. Xi is in the tradition of some of the smoothest moments of relations between the two countries, and it plays to China’s long-held preference to conduct policy through personal relationships.
“Chinese leaders have demonstrated over and over again that they like to operate through personal relationships — like Mao Zedong and Zhou Enlai with Henry Kissinger,” said James Mann, a fellow in residence at Johns Hopkins School of Advanced International Studies and the author of “About Face: A History of America’s Curious Relationship With China, From Nixon to Clinton.”
“It’s a matter of Chinese culture,” Mr. Mann said, “but it also serves their interests, because personalized diplomacy helps them overcome the idea that China should be treated by the same impersonal rules and policies that apply everywhere else.”
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It is not unusual for a new American president to reach out to a foreign leader, even an adversarial one, in an attempt to break a pattern of the past.
Early in his tenure, President George W. Bush praised President Vladimir V. Putin of Russia, saying he had “looked the man in the eye. I found him very straightforward and trustworthy — I was able to get a sense of his soul.”
Former Secretary of State Condoleezza Rice later wrote in her memoir that Mr. Bush’s remark had made him appear gullible. “We were never able to escape the perception that the president had naïvely trusted Putin and then been betrayed,” she said.
Though they come from vastly different worlds, Mr. Xi and Mr. Trump were both born into privilege. Mr. Xi’s father, Xi Zhongxun, was a senior general under Mao during the civil war and helped the Communists come to power. Mr. Trump’s father, Fred C. Trump, was a major New York City builder who left a fortune to his son.
Both men rely on a small group of people to help craft their decisions. For Mr. Xi, Li Zhanshu and Wang Huning, two secretive officials who travel with him everywhere, are said to be the most influential.
For Mr. Trump, his daughter Ivanka, and her husband, Jared Kushner, outstrip everyone else. It is Mr. Kushner who has served as the go-between for Mr. Trump in his dealings with the Chinese. He has convinced his father-in-law of the importance of good relations with China, and encouraged him to play up the personal relationship with Mr. Xi, American analysts familiar with the arrangements said.
Mr. Xi has consistently shown contempt for Kim Jong-un and declined to meet with him, unlike Mr. Trump, who said Monday that he would meet with the North Korean leader if the circumstances were right.
But Mr. Xi’s remoteness from Mr. Kim should not be taken to mean that he will do what Mr. Trump wants and force North Korea to change its behavior, Chinese analysts said.
“There is no possibility for China to fix the situation,” said Shi Yinhong, professor of international relations at Renmin University in Beijing. “That’s because China does not want a nuclear-armed enemy in North Korea.”