Performance in a reaction time task can be strongly influenced by the physical properties of the stimuli used (e.g., position and intensity). The reduction in reaction time observed with higher-intensity visual stimuli has been suggested to arise from reduced processing time along the visual pathway. If this hypothesis is correct, activity should be registered in neurons sooner for higher-intensity stimuli. We evaluated this hypothesis by measuring the onset of neural activity in the intermediate layers of the superior colliculus while monkeys generated saccades to high or low-intensity visual stimuli. When stimulus intensity was high, the response onset latency was significantly reduced compared to low-intensity stimuli. As a result, the minimum time for visually triggered saccades was reduced, accounting for the shorter saccadic reaction times (SRTs) observed following high-intensity stimuli. Our results establish a link between changes in neural activity related to stimulus intensity and changes to SRTs, which supports the hypothesis that shorter SRTs with higher-intensity stimuli are due to reduced processing time.