The role of selective attention in resolving within-object response conflict was explored in a visual-search variant of the Simon task. We asked whether selective attention is required for the suppression of involuntary spatial response activation. In two experiments we systematically introduced delays between target onset and target selection, and between target selection and response. Participants made speeded left or right key-presses to the colour of a target letter O that appeared among varying numbers of nontarget Qs. This difficult search task separated the time of target onset from the time of target selection. Experiment 1 showed that the time course of spatial response suppression was not synched to target onset, but to the time of selective attention to the target. In Experiment 2, the response relevant colour was delayed for variable intervals after the onset of the search array. In this way target selection could occur before the response to the target could be determined. Compatibility effects now decreased with the delay between target selection and the relevant response information. These results show that selective attention is necessary for involuntary response suppression, and they constrain possible models for the control of action in complex environments.