Adaptive behavior requires context-sensitive configuration of task-sets that specify time-varying stimulus-response mappings. Intriguingly, response time costs associated with changing task-sets and motor responses are known to be strongly interactive: switch costs at the task level are small in the presence of a response-switch but large when accompanied by a response-repetition, and vice versa for response-switch costs. The reasons behind this well known interdependence between task- and response-level control processes are currently not well understood. Here, we formalized and tested a model assuming a hierarchical organization of superordinate task-set and subordinate response-set selection processes to account for this effect. The model was found to successfully explain the full range of behavioral task- and response-switch costs across first and second order trial transitions. Using functional magnetic resonance imaging (fMRI) in healthy humans, we then characterized the neural circuitry mediating these effects. We found that presupplementary motor area (preSMA) activity tracked task-set control costs, SMA activity tracked response-set control costs, and basal ganglia (BG) activity mirrored the interaction between task- and response-set regulation processes that characterized participants' response times. A subsequent fMRI-guided transcranial magnetic stimulation experiment confirmed dissociable roles of the preSMA and SMA in determining response costs. Together, these data provide evidence for a hierarchical organization of posterior medial frontal cortex and its interaction with the BG, where a superordinate preSMA-BG loop establishes task-set selection, which imposes a (unidirectional) constraint on a subordinate SMA-BG loop that determines response-selection, resulting in the characteristic interdependence in task- and response-switch costs in behavior.SIGNIFICANCE STATEMENT The ability to use context-sensitive task-sets to guide our responses is central to human adaptive behavior. Task and response selection are strongly interactive: it is more difficult to repeat a response in the context of a changing task-set, and vice versa. However, the neurocognitive architecture giving rise to this interdependence is currently not understood. Here we use modeling, neuroimaging, and noninvasive neurostimulation to show that this phenomenon derives from a hierarchical organization of posterior medial frontal cortex and its interaction with the basal ganglia, where a more anterior corticostriatal loop establishes task-set selection, which constrains a more posterior loop responsible for response-selection. These data provide a neural explanation for a key behavioral signature of human cognitive control.