Considerable progress has been made over the last decades in characterizing the neural coding of hand shape, but grasp force has been largely ignored. We trained two macaque monkeys (Macaca mulatta) on a delayed grasping task where grip type and grip force were instructed. Neural population activity was recorded from areas relevant for grasp planning and execution: the anterior intraparietal area (AIP), F5 of the ventral premotor cortex, and the hand area of the primary motor cortex (M1). Grasp force was strongly encoded by neural populations of all three areas, thereby demonstrating for the first time the coding of grasp force in single- and multi-units of AIP. Neural coding of intended grasp force was most strongly represented in area F5. In addition to tuning analysis, a dimensionality reduction method revealed low-dimensional responses to grip type and grip force. Additionally, this method revealed a high correlation between latent variables of the neural population representing grasp force and the corresponding latent variables of electromyographic forearm muscle activity. Our results therefore suggest an important role of the cortical areas AIP, F5, and M1 in coding grasp force during movement execution as well as of F5 for coding intended grasp force.