Many studies indicate that saccades are necessarily preceded by a shift of attention to the target location. There is no direct evidence for the same coupling during smooth pursuit. If smooth pursuit and attention were coupled, pursuit onset should be delayed whenever attention is focused on a stationary, non-target location. To test this hypothesis, observers were instructed to shift their attention to a peripheral location according to a location cue (Experiments 1 and 2) or a symbolic cue (Experiment 3) around the time of smooth pursuit initiation. Attending to static targets had only negligible effects on smooth pursuit latencies and the early open-loop response but lowered pursuit velocity substantially about the onset of closed-loop pursuit. Around this time, eye velocity reflected the competition between the to-be-tracked and to-be-attended object motion, entailing a reduction of eye velocity by 50% compared to the single task condition. The precise time course of attentional modulation of smooth pursuit initiation was at odds with the idea that an attention shift must precede any voluntary eye movement. Finally, the initial catch-up saccades were strongly delayed with attention diverted from the pursuit target. Implications for models of target selection for pursuit and saccades are discussed.