Minimally delayed (MD) saccades require inhibition of a prepotent response until a target is extinguished, and unlike the more extensively studied antisaccade task, do not require the additional cognitive component of vector inversion (i.e., 180° target spatial transposition). Here, participants completed separate blocks of MD and prepotent stimulus-driven saccades (i.e., respond at target onset) while cortical hemodynamics were measured via functional transcranial Doppler ultrasound. MD saccades produced longer and more variable reaction times (RT). In turn, MD and stimulus-driven saccade preparatory phase cortical hemodynamics increased and decreased, respectively, relative to baseline and the two conditions differed from one another throughout the preparatory phase. The longer RTs and increased cortical hemodynamics of MD saccades is taken to evince response complexity and the increased neural activity to accommodate response inhibition. To our knowledge, such findings provide the first work to examine the neural foundations of MD saccades.