Holding a conversation means that speech must be started, maintained, and stopped continuously. The brain networks that underlie these aspects of speech motor control remain poorly understood. Here we collected functional magnetic resonance imaging (fMRI) data while participants produced normal and fast rate speech in response to sequences of visually presented objects. We took a non-conventional approach to fMRI data analysis that allowed us to study speech motor behavior as it unfolded over time. To this end, whole-brain fMRI signals were extracted in stimulus-locked epochs using slice-based fMRI. These data were then subjected to group independent component analysis to discover spatially independent networks that were associated with different temporal activation profiles. The results revealed two basic brain networks with different temporal dynamics: a cortical network that was activated continuously during speech production, and a second cortico-subcortical network that increased in activity during the initiation and suppression of speech production. Additional analyses explored whether key areas involved in motor suppression such as the right inferior frontal gyrus, sub-thalamic nucleus and pre-supplementary motor area provide first-order signals to stop speech. The results reveal for the first time the brain networks associated with the initiation, maintenance, and suppression of speech motor behavior.