Most sensorimotor studies investigating the covariation of populations of neurons in primary motor cortex (M1) have considered only a few trained movements made under highly constrained conditions. However, motor behaviors in daily living happen in a far more complex and varied contexts. It is unclear whether M1 neurons would have different population responses in a more naturalistic, unconstrained setting, including requirements to accommodate multiple limbs and body posture, and more extensive proprioceptive inputs. Here, we recorded M1 spiking signals while a monkey performed hand grasp movements in two different contexts: one in the typical constrained lab setting, and the other while moving freely in a large plastic cage. We compared the covariance patterns of the neural activity during movements across the two contexts. We found that the neural covariation patterns accompanying two different hand grasps in the unconstrained context were largely preserved, while they differed across contexts, even for the same type of grasp. We also found that the M1 population activity was confined to context-dependent neural manifolds, but these manifolds were not completely independent, as some dimensions appeared to be shared across the contexts. These results suggest that the coordinated activity of M1 neurons is strongly dependent on behavioral context, in ways that were not entirely anticipated.