Although the neural systems that underlie spoken language are well-known, how they adapt to evolving social cues during natural conversations remains an unanswered question. In this work we investigate the neural correlates of face-to-face conversations between two individuals using functional near infrared spectroscopy (fNIRS) and acoustical analyses of concurrent audio recordings. Nineteen pairs of healthy adults engaged in live discussions on two controversial topics where their opinions were either in agreement or disagreement. Participants were matched according to their a priori opinions on these topics as assessed by questionnaire. Acoustic measures of the recorded speech including the fundamental frequency range, median fundamental frequency, syllable rate, and acoustic energy were elevated during disagreement relative to agreement. Consistent with both the a priori opinion ratings and the acoustic findings, neural activity associated with long-range functional networks, rather than the canonical language areas, was also differentiated by the two conditions. Specifically, the frontoparietal system including bilateral dorsolateral prefrontal cortex, left supramarginal gyrus, angular gyrus, and superior temporal gyrus showed increased activity while talking during disagreement. In contrast, talking during agreement was characterized by increased activity in a social and attention network including right supramarginal gyrus, bilateral frontal eye-fields, and left frontopolar regions. Further, these social and visual attention networks were more synchronous across brains during agreement than disagreement. Rather than localized modulation of the canonical language system, these findings are most consistent with a model of distributed and adaptive language-related processes including cross-brain neural coupling that serves dynamic verbal exchanges.