We spend much our lives interacting with others in various social contexts. Although we deal with this myriad of interpersonal exchanges with apparent ease, each one relies upon a broad array of sophisticated cognitive processes. Recent research suggests that the cognitive operations supporting interactive behaviour are themselves underpinned by several canonical functional brain networks (CFNs) that integrate dynamically with one another in response to changing situational demands. Dynamic integrations among these CFNs should therefore play a pivotal role in coordinating interpersonal behaviour. Further, different types of interaction should present different demands on cognitive systems, thereby eliciting distinct patterns of dynamism among these CFNs. To investigate this, the present study performed functional magnetic resonance imaging (fMRI) on 30 individuals while they interacted with one another cooperatively or competitively. By applying a novel combination of analytical techniques to these brain imaging data, we identify six states of dynamic functional connectivity characterised by distinct patterns of integration and segregation among specific CFNs that differ systematically between these opposing types of interaction. Moreover, applying these same states to fMRI data acquired from an independent sample engaged in the same kinds of interaction, we were able to classify interpersonal exchanges as cooperative or competitive. These results provide the first direct evidence for the systematic involvement of CFNs during social interactions, which should guide neurocognitive models of interactive behaviour and investigations into biomarkers for the interpersonal dysfunction characterizing many neurological and psychiatric disorders.