Other officials who have staked a claim to China, such as Secretary of State Rex W. Tillerson and the commerce secretary, Wilbur Ross, have run afoul of Mr. Trump, either on specific policies or broader issues. And Mr. Trump’s national security adviser, Lt. Gen. H. R. McMaster, is not playing the coordinating role on China that several of his predecessors did.

That lack of a guiding hand has contributed to the administration’s dissonant signals toward Beijing. Two months ago, Mr. Ross tried to negotiate a deal with China on steel exports, only to be publicly rebuffed by Mr. Trump. On Sunday, the Treasury secretary, Steven Mnuchin, threatened to cut off trade with any country that does business with North Korea — an unsubtle, and impractical, warning to its main trading partner, China.

“President Xi would like to do something,” Mr. Trump told reporters about their exchange on North Korea. “We’ll see whether or not he can do it. But we will not be putting up with what’s happening in North Korea. I believe that President Xi agrees with me 100 percent.”

But there is little evidence that Mr. Xi will sign on to the steps now being pushed by the United States: a global embargo of oil supplies to North Korea. President Vladimir V. Putin of Russia, who often acts as Mr. Xi’s proxy on these matters, declared that he would oppose such a move in the United Nations Security Council, where Russia holds a veto.

Mr. Xi, a senior Trump administration official said, stuck to his talking points during the call with Mr. Trump. Among them: China was already doing the most it could to pressure North Korea, taking additional steps could create havoc in the region, and the best remedy for the current tension would be for the United States to enter talks with Pyongyang.