Spatial computations underlying the coordination of the hand and eye present formidable geometric challenges. One way for the nervous system to simplify these computations is to directly encode the relative position of the hand and the center of gaze. Neurons in the dorsal premotor cortex (PMd), which is critical for the guidance of arm-reaching movements, encode the relative position of the hand, gaze, and goal of reaching movements. This suggests that PMd can coordinate reaching movements with eye movements. Here, we examine saccade-related signals in PMd to determine whether they also point to a role for PMd in coordinating visual-motor behavior. We first compared the activity of a population of PMd neurons with a population of parietal reach region (PRR) neurons. During center-out reaching and saccade tasks, PMd neurons responded more strongly before saccades than PRR neurons, and PMd contained a larger proportion of exclusively saccade-tuned cells than PRR. During a saccade relative position-coding task, PMd neurons encoded saccade targets in a relative position code that depended on the relative position of gaze, the hand, and the goal of a saccadic eye movement. This relative position code for saccades is similar to the way that PMd neurons encode reach targets. We propose that eye movement and eye position signals in PMd do not drive eye movements, but rather provide spatial information that links the control of eye and arm movements to support coordinated visual-motor behavior.