WASHINGTON—The Pentagon for the first time has set a schedule of naval patrols in the South China Sea in an attempt to create a more consistent posture to counter China’s maritime claims there, injecting a new complication into increasingly uneasy relations between the two powers.

The U.S. Pacific Command has developed a plan to conduct so-called freedom-of-navigation operations two to three times over the next few months, according to several U.S. officials, reinforcing the U.S. challenge to what it sees as excessive Chinese...