Intentional inhibition, the endogenous decision to stop or cancel an action, is arguably a more ecologically valid process than automatized, reactive, inhibition which occurs in response to an external stop signal without active decision making at the moment of inhibition. Choosing to stop an act of opening the fridge door, or of reaching for a bottle of alcohol may therefore extend beyond a reactive inhibitory process, e.g. stopping at a red traffic light. Existing paradigms of intentional inhibition focus on the proportions of intentional stops. Here we developed the Intentional Hand Task, which provides stop response times for intentional and instructed trials. Participants move a cursor by initiating an arm movement, after which a Go, Stop or Choice trial occurs. In Go trials, participants are instructed to make a speeded continuation of their arm movement towards a target whereas in the Stop trials participants are instructed to rapidly stop the already initiated movement. In Choice trials, participants chose whether to continue or stop the movement. By comparing response times when movement was stopped, we found that intentionally stopping took significantly longer than externally instructed stopping. We further investigated the influence of reward incentives, by cueing trials with either the prospect of No, Low or High reward for correctly continuing in Go trials, stopping in Stop trials or achieving a random balance of intentional Go and Stops in Choice trials. Reward incentives led to greater approach behaviours, indicated by significantly higher Go accuracy in instructed Go trials and faster response times across both Go trial types. The presence of reward incentives led to significantly fewer intentional stop choices. Our findings suggest intentional inhibition of an ongoing action may require a further decisional process. Furthermore, monetary incentives may implicitly trigger an appetitive system thus facilitating approach rather than intentional inhibitory behaviour. These findings are particularly relevant to cue-related relapse in disorders of addiction where cues may facilitate approach behaviours to the detriment of intentional inhibitory control.