Mr. Kushner first made his influence felt in early February when he and Mr. Cui orchestrated a fence-mending phone call between Mr. Trump and Mr. Xi. During that exchange, Mr. Trump pledged to abide by the four-decade-old “One China” policy on Taiwan, despite his earlier suggestion that it was up for negotiation.

Now, officials said, Mr. Trump wants something in return: He plans to press Mr. Xi to intensify economic sanctions against North Korea to pressure the country to shut down its nuclear weapons and ballistic missile programs. He has also vowed to protest the chronic trade imbalance between the United States and China, which he railed against during his presidential campaign.

China’s courtship of Mr. Kushner, which has coincided with the marginalization of the State Department in the Trump administration, reflects a Chinese comfort with dynastic links. Mr. Xi is himself a “princeling”: His father was Xi Zhongxun, a major figure in the Communist revolution who was later purged by Mao Zedong.