The precise quantification of time during motor performance is critical for many complex behaviors, including musical execution, speech articulation, and sports; however, its neural mechanisms are primarily unknown. We found that neurons in the medial premotor cortex (MPC) of behaving monkeys are tuned to the duration of produced intervals during rhythmic tapping tasks. Interval-tuned neurons showed similar preferred intervals across tapping behaviors that varied in the number of produced intervals and the modality used to drive temporal processing. In addition, we found that the same population of neurons is able to multiplex the ordinal structure of a sequence of rhythmic movements and a wide range of durations in the range of hundreds of milliseconds. Our results also revealed a possible gain mechanism for encoding the total number of intervals in a sequence of temporalized movements, where interval-tuned cells show a multiplicative effect of their activity for longer sequences of intervals. These data suggest that MPC is part of a core timing network that uses interval tuning as a signal to represent temporal processing in a variety of behavioral contexts where time is explicitly quantified.