BEIJING—The mayor of Wuhan, the city at the epicenter of China’s viral outbreak, said rules imposed by Beijing limited what he could disclose about the threat posed by the pathogen, suggesting the central government was partially responsible for a lack of transparency that has marred the response to the fast-expanding health crisis.

Mayor Zhou Xianwang’s comments were broadcast on China’s state television network hours after Premier Li Keqiang arrived in the city to meet infected patients and front-line health workers—an attempt...