Competitive and cooperative interactions are based on anticipation or synchronization with the partner's actions. Both forms of interaction may either require performing imitative or complementary movements with respect to those performed by our partner. We explored how parietal regions involved in the control of imitative behavior (temporo-parietal junction, TPJ), goal coding and visuo-motor integration (anterior intraparietal sulcus, aIPS) contribute to the execution of imitative and complementary movements during cooperative and competitive interactions. To this aim, we delivered off-line non-invasive inhibitory brain stimulation to healthy individuals' left aIPS and right TPJ before they were asked to reach and grasp an object together with a virtual partner by either performing imitative or complementary interactions. In different blocks, participants were asked to compete or cooperate with the virtual partner that varied its behavior according to cooperative or competitive contexts. Left aIPS and right TPJ inhibition impaired individuals' performance (i.e., synchrony in cooperative task and anticipation in competition) during complementary and imitative interactions, respectively, in both cooperative and competitive contexts, indicating that aIPS and TPJ inhibition affects own-other action integration and action imitation (that are different in complementary vs imitative interactions) more than action synchronization or anticipation (that are different in cooperative vs competitive contexts).