A spatiotemporal pattern of excitability propagates across the primary motor cortex prior to the onset of a reaching movement in non-human primates. If this pattern is a necessary component of voluntary movement initiation, it should be present across a variety of motor tasks, end-effectors, and even species. Here, we show that propagating patterns of excitability occur during the initiation of precision grip force and tongue protrusion in non-human primates, and even isometric wrist extension in a human participant. In all tasks, the directions of propagation across the cortical sheet were bimodally distributed across trials with modes oriented roughly opposite to one another. Propagation speed was unimodally distributed with similar mean speeds across tasks and species. Additionally, propagation direction and speed did not vary systematically with any behavioral measures except response times indicating that this propagating pattern is invariant to kinematic or kinetic details and may be a generic movement initiation signal.