The interpretation of social cues is a fundamental function of human social behavior, and resolution of inconsistencies between spoken and gestural cues plays an important role in successful interactions. To gain insight into these underlying neural processes, we compared neural responses in a traditional color/word conflict task and to a gesture/word conflict task to test hypotheses of domain-general and domain-specific conflict resolution. In the gesture task, recorded spoken words ("yes" and "no") were presented simultaneously with video recordings of actors performing one of the following affirmative or negative gestures: thumbs up, thumbs down, head nodding (up and down), or head shaking (side-to-side), thereby generating congruent and incongruent communication stimuli between gesture and words. Participants identified the communicative intent of the gestures as either positive or negative. In the color task, participants were presented the words "red" and "green" in either red or green font and were asked to identify the color of the letters. We observed a classic "Stroop" behavioral interference effect, with participants showing increased response time for incongruent trials relative to congruent ones for both the gesture and color tasks. Hemodynamic signals acquired using functional near-infrared spectroscopy (fNIRS) were increased in the right dorsolateral prefrontal cortex (DLPFC) for incongruent trials relative to congruent trials for both tasks consistent with a common, domain-general mechanism for detecting conflict. However, activity in the left DLPFC and frontal eye fields and the right temporal-parietal junction (TPJ), superior temporal gyrus (STG), supramarginal gyrus (SMG), and primary and auditory association cortices was greater for the gesture task than the color task. Thus, in addition to domain-general conflict processing mechanisms, as suggested by common engagement of right DLPFC, socially specialized neural modules localized to the left DLPFC and right TPJ including adjacent homologous receptive language areas were engaged when processing conflicting communications. These findings contribute to an emerging view of specialization within the TPJ and adjacent areas for interpretation of social cues and indicate a role for the region in processing social conflict.