Smooth pursuit is punctuated by catch-up saccades, which are thought to automatically correct sensory errors in retinal position and velocity. Recent studies have shown that the timing of catch-up saccades is susceptible to cognitive modulation, as is the timing of fixational microsaccades. Are the timing of catchup and microsaccades thus modulated by the same mechanism? Here, we test directly whether pursuit catch-up saccades and fixational microsaccades exhibit the same temporal pattern of task-related bursts and subsidence. Observers pursued a linear array of 15 alphanumeric characters that translated across the screen and simultaneously performed a character identification task on it. At a fixed time, a cue briefly surrounded the central element to specify it as the pursuit target. After a random delay, a probe (E or 3) appeared briefly at a randomly selected character location, and observers identified it. For comparison, a fixation condition was also tested with trial parameters identical to the pursuit condition, except that the array remained stationary. We found that during both pursuit and fixation tasks, saccades paused after the cue and then rebounded as expected but also subsided in anticipation of the task. The time courses of the reactive pause, rebound, and anticipatory subsidence were similar, and idiosyncratic subject behavior was consistent across pursuit and fixation. The results provide evidence for a common mechanism of saccade control during pursuit and fixation, which is predictive as well as reactive and has an identifiable temporal signature in individual observers. NEW & NOTEWORTHY During natural scene viewing, voluntary saccades reorient the fovea to different locations for high-acuity viewing. Less is known about small “microsaccades” that also occur when fixating stationary objects and “catch-up saccades” that occur during smooth pursuit of moving objects. We provide evidence that microsaccade and catch-up saccade frequencies are generally modulated by the same mechanism. Furthermore, on a finer time scale the mechanism operates differently in different observers, suggesting that neural saccade generators are individually unique.