The default network exhibits correlated activity at rest and has shown decreased activation during performance of cognitive tasks. There has been little investigation of changes in connectivity of this network during task performance. In this study, we examined task-related modulation of connectivity between two seed regions from the default network posterior cingulated cortex (PCC) and medial prefrontal cortex (mPFC) and the rest of the brain in 12 healthy adults. The purpose was to determine (1) whether connectivity within the default network differs between a resting state and performance of a cognitive (working memory) task and (2) whether connectivity differs between these nodes of the default network and other brain regions, particularly those implicated in cognitive tasks. There was little change in connectivity with the other main areas of the default network for either seed region, but moderate task-related changes in connectivity occurred between seed regions and regions outside the default network. For example, connectivity of the mPFC with the right insula and the right superior frontal gyrus decreased during task performance. Increased connectivity during the working memory task occurred between the PCC and bilateral inferior frontal gyri, and between the mPFC and the left inferior frontal gyrus, cuneus, superior parietal lobule, middle temporal gyrus and cerebellum. Overall, the areas showing greater correlation with the default network seed regions during task than at rest have been previously implicated in working memory tasks. These changes may reflect a decrease in the negative correlations occurring between the default and task-positive networks at rest.