American officials, who would not be named talking about the continuing dialogue with the Chinese, said they hoped the tough steps by the United States would spur Mr. Xi to reconsider his reluctance to press the North. But Mr. Trump, one official said, now has fewer illusions that China will radically alter its approach to its reclusive neighbor, which is driven more by fear of a chaotic upheaval there than by concern about its nuclear and missile programs.
That leaves the president in a familiar bind on North Korea as he prepares to leave for a Group of 20 meeting this week in Germany, where he will meet Mr. Xi as well as the leaders of Japan and South Korea, nations Mr. Trump has also turned to in navigating his approach to the North.
Without the full weight of China, pressure tactics are unlikely to force North Korea’s leader, Kim Jong-un, to change course. Yet diplomatic engagement — which Mr. Xi continues to push, according to officials — is not a step that Mr. Trump is ready to consider, after the death last month of an American college student, Otto F. Warmbier, who was held captive in Pyongyang for 17 months, then freed in a coma.
A go-it-alone approach by Mr. Trump would also further antagonize China, since it would require blacklisting multiple Chinese banks and companies that do business with the North. The United States began doing so on a modest scale last week by designating four Chinese entities and individuals.
The precarious state of United States-China relations was captured by the way the two sides characterized the call. The White House said only that Mr. Trump had raised the “growing threat” of North Korea’s weapons programs with Mr. Xi. The Chinese, in a more detailed statement, said the relationship was being “affected by some negative factors.”
The latest of these — and perhaps the most grating to the Chinese — was a naval maneuver in which an American guided-missile destroyer sailed near disputed territory claimed by Beijing in the South China Sea. The movement by the warship, the Stethem, off Triton Island in the Paracel archipelago prompted a furious response from China’s government, which called it a “serious political and military provocation.”
Still, neither leader appeared ready to abandon the rapport that Mr. Trump and Mr. Xi established in April at a summit meeting in Palm Beach, Fla. Mr. Trump avoided any personal jabs at Mr. Xi; the Chinese government said tensions were to be expected in a relationship this complex. But each leader has learned a hard lesson about the other, according to officials and outside analysts.
Mr. Xi, they said, miscalculated what China needed to do to satisfy Mr. Trump, thinking he could buy him off with a few highly visible measures, like banning coal purchases from the North. Mr. Trump overvalued the personal touch by betting that a few hearty handshakes with Mr. Xi would overcome China’s deep-rooted resistance to pressuring North Korea.
“The Chinese tried to figure out what was the absolute minimum they needed to do,” said Bonnie S. Glaser, director of the China Power Project at the Center for Strategic and International Studies. “The administration has signaled repeatedly that they had to shut down these banks and front companies in northeast China that enable North Korea.”
Chinese officials professed surprise last week when the White House rolled out three tough steps, back to back. It imposed sanctions on a Chinese bank, accusing it of acting as a conduit for illicit North Korean financial activity, as well as on a Chinese company and two Chinese citizens.
It approved the sale of $1.4 billion in weapons to Taiwan, which China regards as a breakaway province. And it labeled China one of the worst offenders in an annual State Department report on human trafficking.
The White House also signaled it would act against imported Chinese steel as part of a broader campaign against steel dumping around the world. But the Commerce Department’s report on the steel market, which would be the basis for tariffs and other sanctions, is still undergoing revisions and will not be released before the Group of 20 meeting.
The American destroyer’s cruise past Triton appeared to be especially offensive to China. It was only the second time since Mr. Trump took office in January that an American warship had ignored China’s claims in the South China Sea. On May 24, another guided-missile destroyer, the Dewey, traversed Mischief Reef in the disputed Spratly Islands.
“The Chinese side strongly urges the U.S. side to immediately stop such kind of provocative operations that violate China’s sovereignty and threaten China’s security,” a Foreign Ministry spokesman, Lu Kang, said on Sunday. “The Chinese side will continue to take all necessary means to defend national sovereignty and security.”
Washington and Beijing confirmed that Mr. Trump requested the call on Sunday. But American officials said their Chinese counterparts signaled that they were eager to clear the air after a bumpy week.
Cheng Xiaohe, an associate professor of international relations at Renmin University in Beijing, said it was “a little bit odd” that Mr. Xi had agreed to the call. Still, he said, the gesture indicated that China was seeking to maintain “stability and some momentum” with Mr. Trump and perhaps deter him from taking more extreme measures, such as military action.
“The actions the administration has taken have upset the Chinese, no doubt about it,” Professor Cheng said. “The conversations demonstrate that China is still willing to talk with Trump and work with the U.S. government to deal with North Korea’s nuclear issues.”
China’s resistance has led Mr. Trump to turn to other nations, notably Japan and South Korea, for help in resolving the crisis.
He had a warmer call with Prime Minister Shinzo Abe of Japan, who praised his decision to penalize Chinese entities accused of doing illicit business with the North, according to Kyodo News, a Japanese news agency. Mr. Trump will host a dinner with Mr. Abe and Moon Jae-in, South Korea’s new president, at the Group of 20 in Hamburg on Thursday.
Some former officials said the tensions between Mr. Trump and Mr. Xi were neither new nor particularly troubling.
“We’ve had similar dynamics under Bush, Clinton and Obama,” said Jeffrey A. Bader, a China adviser to President Barack Obama. “It’s not an either-or. We operate in a nether zone with the Chinese.”