In the visual world, stimuli compete with each other for allocation of the brain's limited processing resources. Computational models routinely invoke wide-ranging mutually suppressive interactions in spatial priority maps to implement active competition for attentional and saccadic allocation, but such suppressive interactions have not been physiologically described, and their existence is controversial. Much evidence implicates the lateral intraparietal area as a candidate priority map in the macaque (Macaca mulatta). Here, we demonstrate that the responses of neurons in the lateral intraparietal area (LIP) to a task-irrelevant distractor are strongly suppressed when the monkey plans saccades to locations outside their receptive fields. Suppression can be evoked both by flashed visual stimuli and by a memorized saccade plan. The suppressive surrounds of LIP neurons are spatially tuned and wide ranging. Increasing the monkey's motivation enhances target-distractor discriminability by enhancing both distractor suppression and the saccade goal representation; these changes are accompanied by correlated improvements in behavioral performance.