Automatic imitation of observed actions is thought to be a powerful mechanism, one that may mediate the reward value of interpersonal interactions, but that could also generate visuo-motor interference when interactions involve complementary movements. Since interpersonal coordination seems to be crucial both when cooperating and competing with others, the questions arises as to whether imitation-and thus visuo-motor interference-occurs in both scenarios. To address this issue, we asked human participants to engage in high- or low-interactive (Interactive or Cued condition, respectively), cooperative or competitive, joint reach-to-grasps with a virtual partner. More specifically, interactions occurred in: (i) a Cued condition, where participants simply adapted their movement timing to synchronize with (during cooperation) or anticipate (during competition) the virtual partner's grasp; (ii) an Interactive condition requiring the same adaptation, as well as a real-time selection of their action according to the virtual character's movement. To simulate a realistic human-human interaction, the virtual character would change its movement speed in consecutive trials according to participants' behaviour. Results demonstrate that visuo-motor interference-as indexed by movement kinematics (higher maximum wrist height during complementary compared to imitative power grips)-emerge in both cooperative and competitive motor interactions only when predictions about the partner's movements are needed to perform one's own action (interactive condition). These results support the idea that simulative imitation is heavily present when individuals need to match their behaviours closely.