The U.S. conducted a naval patrol close to a China-controlled island in the South China Sea on Sunday—the second such operation confirmed by American officials in less than six weeks—following several recent moves that appear to signal Washington’s displeasure with Beijing.

The U.S. Navy on Sunday sent the guided-missile destroyer USS Stethem near Triton Island in the Paracel Island chain in the South China Sea, according to U.S. officials. The warship came to within 12 nautical miles of Triton, indicating the patrol was...