Animals use a combination of eye movements to track moving objects. These different eye movements need to be coordinated for successful tracking, requiring interactions between the systems involved. Here, we study the interaction between the saccadic and smooth pursuit eye movement systems in marmosets. Using a single-target pursuit task, we show that saccades cause an enhancement in pursuit following a saccade. Using a two-target pursuit task, we show that this enhancement in pursuit is selective toward the motion of the target selected by the saccade, irrespective of any biases in pursuit prior to the saccade. These experiments highlight the similarities in the functioning of saccadic and smooth pursuit eye movement systems across primates.