Within our societies, humans form co-operative groups with diverse levels of relationship quality among individual group members. In establishing relationships with others, we use attitudes and beliefs about group members and the group as a whole to establish relationships with particular members of our social networks. However, we have yet to understand how brain responses to group members facilitate relationship quality between pairs of individuals. We address this here using a round-robin interpersonal perception paradigm in which each participant was both a perceiver and target for every other member of their group in a set of 20 unique groups of between 5 and 6 members in each (total N = 111). Using functional magnetic resonance imaging, we show that measures of social relationship strength modulate the brain-to-brain multivoxel similarity patterns between pairs of participants’ responses when perceiving other members of their group in regions of the brain implicated in social cognition. These results provide evidence for a brain mechanism of social cognitive processes serving interpersonal relationship strength among group members.