Fisheries can profoundly impact co‐occurring species exposed to incidental capture. Spatiotemporal fisheries management holds substantial potential to balance socioeconomic benefits with ecological costs to threatened bycatch species. This study estimated the effect of the spatial and temporal distribution of effort by a western Pacific Ocean tuna purse seine fishery on catch rates of target and at‐risk species by fitting spatially explicit generalized additive multilevel regression models within a Bayesian inference framework to observer data. Mean field prediction surfaces defined catch rate hotspots for tunas, silky sharks, rays, and whale sharks, informing the design of candidate area‐based management strategies. Due to limited sample sizes, odontocete and marine turtle catch rate geospatial patterns were summarized using simple 2D hexagonal binning. Effort could be focused in two areas within core fishing grounds to reduce overlap with hotspots for silky sharks, rays, and whale sharks without affecting target catch. Effort could be shifted outside of core fishing areas to zones with higher target tuna catch rates to reduce overlap with hotspots for at‐risk species. Sparse and small marine turtle and whale shark hotspots occurred across the fishing grounds. Results did not identify opportunities for temporally dynamic spatial management to balance target and at‐risk catch rates. Research on the economic and operational viability of alternative spatial management strategies is a priority. A small subset of sets had disproportionately large odontocete captures. Real‐time fleet communication, move‐on rules, and avoiding sets on dolphin schools might reduce odontocete catch rates. Managing set association type and mesh size present additional opportunities to balance catch rates of at‐risk and target species. Employing output controls that effectively constrain the fishery would alter the spatial management strategy to focus fishing within zones with the lowest ratio of at‐risk bycatch to target tuna catch. Findings inform the design of alternative spatial management strategies to avoid catch rate hotspots of at‐risk species without compromising the catch of principal market species.