BEIJING—China said it staged maritime defense exercises in the South China Sea, just four days after Vietnam conducted live-fire drills in the same disputed waters, the latest development in an escalating confrontation between Beijing and two of its Southeast Asian neighbors.

The announcement came as Philippine President Benigno Aquino III warned China, in an interview with the Associated Press, not to intrude into waters claimed by Manila, saying his country wouldn't be bullied by Beijing in the dispute...