Corrective responses to limb disturbances are surprisingly complex, but the neural basis of these goal-directed responses is poorly understood. Here we show that somatosensory feedback is transmitted to many sensory and motor cortical regions within 25 ms of a mechanical disturbance applied to the monkey’s arm. When limb feedback was salient to an ongoing motor action (task engagement), neurons in parietal area 5 immediately (~25 ms) increased their response to limb disturbances, whereas neurons in other regions did not alter their response until 15 to 40 ms later. In contrast, initiation of a motor action elicited by a limb disturbance (target selection) altered neural responses in primary motor cortex ~65 ms after the limb disturbance, and then in dorsal premotor cortex, with no effect in parietal regions until 150 ms post-perturbation. Our findings highlight broad parietofrontal circuits that provide the neural substrate for goal-directed corrections, an essential aspect of highly skilled motor behaviors.