The contributions of the cerebral cortex to human balance control are clearly demonstrated by the profound impact of cortical lesions on the ability to maintain standing balance. The cerebral cortex is thought to regulate subcortical postural centers to maintain upright balance and posture under varying environmental conditions and task demands. However, the cortical mechanisms that support standing balance remain elusive. Here, we present an EEG-based analysis of cortical oscillatory dynamics during the preparation and execution of balance responses with distinct postural demands. In our experiment, participants responded to backward movements of the support surface either with one forward step or by keeping their feet in place. To challenge the postural control system, we applied participant-specific high accelerations of the support surface such that the postural demand was low for stepping responses and high for feet-in-place responses. We expected that postural demand modulated the power of intrinsic cortical oscillations. Independent component analysis and time-frequency domain statistics revealed stronger suppression of alpha (9–13 Hz) and low-gamma (31–34 Hz) rhythms in the supplementary motor area (SMA) when preparing for feet-in-place responses (i.e., high postural demand). Irrespective of the response condition, support-surface movements elicited broadband (3–17 Hz) power increase in the SMA and enhancement of the theta (3–7 Hz) rhythm in the anterior prefrontal cortex (PFC), anterior cingulate cortex (ACC), and bilateral sensorimotor cortices (M1/S1). Although the execution of reactive responses resulted in largely similar cortical dynamics, comparison between the bilateral M1/S1 showed that stepping responses corresponded with stronger suppression of the beta (13–17 Hz) rhythm in the M1/S1 contralateral to the support leg. Comparison between response conditions showed that feet-in-place responses corresponded with stronger enhancement of the theta (3–7 Hz) rhythm in the PFC. Our results provide novel insights into the cortical dynamics of SMA, PFC, and M1/S1 during the control of human balance.