SINGAPORE—The U.S. and China appear to be headed for a more confrontational relationship in Southeast Asia as Washington warns of a more aggressive response to the militarization of disputed islands in the South China Sea.

Speaking at the Shangri-La Dialogue, a regional security conference, U.S. Defense Secretary Jim Mattis warned there could be “much larger consequences” in the future from China’s moves to install weapons systems on islands in the sea. He didn’t specify what the consequences would be.

The...