HONG KONG — In terms of publicity, it was a great weekend for Mark Zuckerberg in China.

Mr. Zuckerberg, the Facebook founder, returned to Beijing for yet another trip that drew local headlines and captivated online China. He wrote a post that went viral about a jog through Tiananmen Square; held a widely covered conversation with China's best-known entrepreneur, Jack Ma of Alibaba; and on Saturday met with one of the most powerful men in China, Liu Yunshan, the country's propaganda chief.

It followed previous trips in which Mr. Zuckerberg impressed Chinese audiences with his rookie Chinese language skills and spoke about his fascination with the country. Even at times while he was outside China, he met with China's president, Xi Jinping; told a Chinese official he was reading a book of Mr. Xi's words and gave his newborn daughter, Max, a Chinese name. (It is Chen Mingyu.)

The visits have cemented his place as one of the best-known foreign business executives in China. But it is far from clear whether his charm offensive will unlock Mr. Zuckerberg's ultimate goal: persuading the Chinese government to lift its ban on the social media service and open it to the country's almost 700 million Internet users.

Courting Chinese leaders in such a public fashion is an unusual strategy for a foreign executive. With star power comes influence, and any clout not directly controlled by the Chinese Communist Party can be deemed dangerous. China demonstrated this last month, when a widely read social media account of a prominent real estate tycoon disappeared after he criticized Mr. Xi's call for unswerving loyalty from the country's media.

The few American technology firms that have entered China in recent years have played down their efforts. Though Travis Kalanick, a founder of Uber, frequently travels to China, news of his presence rarely spreads across the Chinese Internet. There was almost no fanfare in advance of LinkedIn's deal with two closely connected Chinese venture capital shops to enter China, an event that was marked with a blog post.

If Mr. Zuckerberg succeeds, it could show other foreign companies blocked in China that they have a potential path into the huge and fast-growing market — one that calls for them to accept China's strict controls on discourse and to refrain from rocking the boat. A failure would underscore Chinese distrust of foreign technology companies and cement the idea that the low-profile approach is the only way to gain market access.