SHANGHAI—After repeated and unheeded warnings to China to halt its massive reclamation works in the South China Sea, the U.S. is contemplating an option fraught with danger: limited, but direct, military action.

By sending U.S. warplanes over artificial islands that China is building, and sailing naval vessels close by—an option now under consideration, according to U.S. officials in Washington—America could end up being sucked more deeply into an increasingly heated territorial dispute between China and its neighbors, say...