BEIJING—A senior Chinese official in charge of Hong Kong affairs warned that Beijing would intervene if the local government proved unable to contain the violent protests, the most explicit threat of intervention to date from the central government.

At a meeting with Hong Kong representatives in the nearby city of Shenzhen on Wednesday, the official, Zhang Xiaoming, issued a dire assessment of the situation in the territory after more than two months of protests. He called the situation the most severe since China resumed...