We investigated the flexible modulation of undirected functional connectivity (uFC) of brain pathways during simple uni-manual responding. Two questions were central to our interests: (1) does response hand (dominant vs. non-dominant) differentially modulate connectivity and (2) are these effects related to responding under varying motor sets. fMRI data were acquired in twenty right-handed volunteers who responded with their right (dominant) or left (non-dominant) hand (blocked across acquisitions). Within acquisitions, the task oscillated between periodic responses (promoting the emergence of motor sets) or randomly induced responses (disrupting the emergence of motor sets). Conjunction analyses revealed eight shared nodes across response hand and condition, time series from which were analyzed. For right hand responses connectivity of the M1 ←→ Thalamus and SMA ←→ Parietal pathways was more significantly modulated during periodic responding. By comparison, for left hand responses, connectivity between five network pairs (including M1 and SMA, insula, basal ganglia, premotor cortex, parietal cortex, thalamus) was more significantly modulated during random responding. uFC analyses were complemented by directed FC based on multivariate autoregressive models of times series from the nodes. These results were complementary and highlighted significant modulation of dFC for SMA → Thalamus, SMA → M1, basal ganglia → Insula and basal ganglia → Thalamus. The results demonstrate complex effects of motor organization and task demand and response hand on different connectivity classes of fMRI data. The brain's sub-networks are flexibly modulated by factors related to motor organization and/or task demand, and our results have implications for assessment of medical conditions associated with motor dysfunction.