Verbal communication relies heavily upon mutual understanding, or common ground. Inferring the intentional states of our interaction partners is crucial in achieving this, and social neuroscience has begun elucidating the intra- and inter-personal neural processes supporting such inferences. Typically, however, neuroscientific paradigms lack the reciprocal to-and-fro characteristic of social communication, offering little insight into the way these processes operate online during real-world interaction. In the present study, we overcame this by developing a "hyperscanning" paradigm in which pairs of interactants could communicate verbally with one another in a joint-action task whilst both undergoing functional magnetic resonance imaging simultaneously. Successful performance on this task required both interlocutors to predict their partner's upcoming utterance in order to converge on the same word as each other over recursive exchanges, based only on one another's prior verbal expressions. By applying various levels of analysis to behavioural and neuroimaging data acquired from 20 dyads, three principal findings emerged: First, interlocutors converged frequently within the same semantic space, suggesting that mutual understanding had been established. Second, assessing the brain responses of each interlocutor as they planned their upcoming utterances on the basis of their co-player's previous word revealed the engagement of the temporo-parietal junctional (TPJ), precuneus and dorso-lateral pre-frontal cortex. Moreover, responses in the precuneus were modulated positively by the degree of semantic convergence achieved on each round. Second, effective connectivity among these regions indicates the crucial role of the right TPJ in this process, consistent with the Nexus model. Third, neural signals within certain nodes of this network became aligned between interacting interlocutors. We suggest this reflects an interpersonal neural process through which interactants infer and align to one another's intentional states whilst they establish a common ground.