Grasping is a highly complex movement that requires the coordination of multiple hand joints and muscles. Muscle synergies have been proposed to be the functional building blocks that coordinate such complex motor behaviors, but little is known about how they are implemented in the central nervous system. Here we demonstrate that premotor interneurons (PreM-INs) in the primate cervical spinal cord underlie the spatiotemporal patterns of hand muscle synergies during a voluntary grasping task. Using spike-triggered averaging of hand muscle activity, we found that the muscle fields of PreM-INs were not uniformly distributed across hand muscles but rather distributed as clusters corresponding to muscle synergies. Moreover, although individual PreM-INs have divergent activation patterns, the population activity of PreM-INs reflects the temporal activation of muscle synergies. These findings demonstrate that spinal PreM-INs underlie the muscle coordination required for voluntary hand movements in primates. Given the evolution of neural control of primate hand functions, we suggest that spinal premotor circuits provide the fundamental coordination of multiple joints and muscles upon which more fractionated control is achieved by superimposed, phylogenetically newer, pathways.