The extinction of a previously conditioned response can be modulated through cognitive processes, including feature-based information, and explicit instruction. Here, we introduce a selective extinction through cognitive evaluation (SECE) task in which information is cognitively evaluated on a trial-by-trial basis to ascertain the extinction contingencies. Participants were conditioned to expect an electric shock during the presentation of one of two letters (CS+/CS-). During the SECE task, the letters were presented within words belonging to two categories, one of which indicated safety (COG-_CS+ trials), while risk of shock was maintained for the other category (COG+_CS+ trials). Skin conductance responses indicated that participants reduced their response to COG-_CS+ trials compared to COG+_CS+ trials. Clusters in bilateral insula and anterior cingulate cortex showed activation for COG+_CS+ trials that was reduced for COG-_CS+ trials. A network of brain regions, including left inferior frontal gyrus, and bilateral temporal and parietal cortices showed greater activation for COG-_CS+ versus COG+_CS+ trials. This is consistent with the semantic processing and decision-making necessary to evaluate the trial contingencies. We compared activation in the SECE task to activation in a cognitive reappraisal task in which participants were asked to attend to, or regulate their emotional reactions to affective IAPS images. This task replicated prefrontal activation seen in previous reappraisal studies. A voxelwise conjunction analysis found no overlap between the cognitive reappraisal and the SECE task, but we did find evidence for common activation in follow-up ROI analyses, supporting the idea of common lateral prefrontal mechanisms involved in both processes.