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Physical activity and cognitive functioning are strongly intertwined. However, the causal relationships underlying this association are still unclear. Physical activity can enhance brain functions, but healthy cognition may also promote engagement in physical activity. Here, we assessed the bidirectional relationships between physical activity and general cognitive functioning using Latent Heritable Confounder Mendelian Randomization (LHC-MR). Association data were drawn from two large-scale genome-wide association studies (UK Biobank and COGENT) on accelerometer-measured moderate, vigorous, and average physical activity (N = 91,084) and cognitive functioning (N = 257,841). After Bonferroni correction, we observed significant LHC-MR associations suggesting that increased fraction of both moderate (b = 0.32, CI95% = [0.17,0.47], P = 2.89e − 05) and vigorous physical activity (b = 0.22, CI95% = [0.06,0.37], P = 0.007) lead to increased cognitive functioning. In contrast, we found no evidence of a causal effect of average physical activity on cognitive functioning, and no evidence of a reverse causal effect (cognitive functioning on any physical activity measures). These findings provide new evidence supporting a beneficial role of moderate and vigorous physical activity (MVPA) on cognitive functioning. [ABSTRACT FROM AUTHOR]