We investigated how verbal communication with a robot differs from talking to a human in terms of brain activity by analysing an open-source fMRI dataset. We focused on modeling conversational dynamics rather than conversation as a whole, by analysing fine-grained events, in particular turn initiation. The results indicate that turn initiation in a conversation with a human involves higher activation in auditory and visual cortex than turn initiation with a robot. Conversely, listening to the robot showed higher engagement of auditory cortex than listening to a human. We suggest that verbal and non-verbal turn-taking cues provided by the human agent engage more cognitive processing for picking up the turn. On the other hand, listening to a robot agent requires more processing than listening to a human. Both findings suggest that the accurate simulation of appropriate turn-taking cues and behaviors will help robots to establish more natural conversation dynamics and that the use of brain imaging can provide valuable objective measurements for assessing user states in human-robot interaction.