Over the last two decades, inhibitory control has featured prominently in accounts of how humans and other organisms regulate their behaviour and thought. Previous work on how the brain stops actions and thoughts, however, has emphasised distinct prefrontal regions supporting these functions, suggesting domain-specific mechanisms. Here we show that stopping actions and thoughts recruits common regions in the right dorsolateral and ventrolateral prefrontal cortex to suppress diverse content, via dynamic targeting. Within each region, classifiers trained to distinguish action-stopping from action-execution also identify when people are suppressing their thoughts (and vice versa). Effective connectivity analysis reveals that both prefrontal regions contribute to action and thought stopping by targeting the motor cortex or the hippocampus, depending on the goal, to suppress their task-specific activity. These findings support the existence of a domain-general system that underlies inhibitory control and establish Dynamic Targeting as a mechanism enabling this ability.