China’s securities regulator issued its strongest warning yet about the country’s soaring stock markets and tightened rules on margin lending, while the country’s two stock exchanges said they would make it easier to bet against stocks, spurring worries that the world’s best-performing markets could tumble.

The announcements late Friday by the China Securities Regulatory Commission, the Shanghai and Shenzhen stock exchanges and two industry associations raised fears of a selloff in China, where the main market index has doubled...