Eye movements challenge the perception of a stable world by inducing retinal image displacement. During saccadic eye movements visual stability is accompanied by a remapping of visual receptive fields, a compression of visual space and perceptual suppression. Here we explore whether a similar suppression changes the perception of briefly presented low contrast targets during the initiation of smooth pursuit eye movements. In a 2AFC design we investigated the contrast sensitivity for threshold-level stimuli during the initiation of smooth pursuit and during saccades. Pursuit was elicited by horizontal step-ramp and ramp stimuli. At any time from 200 ms before to 500 ms after pursuit stimulus onset, a blurred 0.3 deg wide horizontal line with low contrast just above detection threshold appeared for 10 ms either 2 deg above or below the pursuit trajectory. Observers had to pursue the moving stimulus and to indicate whether the target line appeared above or below the pursuit trajectory. In contrast to perceptual suppression effects during saccades, no pronounced suppression was found at pursuit onset for step-ramp motion. When pursuit was elicited by a ramp stimulus, pursuit initiation was accompanied by catch-up saccades, which caused saccadic suppression. Additionally, contrast sensitivity was attenuated at the time of pursuit or saccade stimulus onset. This attenuation might be due to an attentional deficit, because the stimulus required the focus of attention during the programming of the following eye movement.