Primates heavily rely on their visual system, which exploits signals of graded precision based on the eccentricity of the target in the visual field. The interactions with the environment involve actively selecting and focusing on visual targets or regions of interest, instead of contemplating an omnidirectional visual flow. Eye-movements specifically allow foveating targets and track their motion. Once a target is brought within the central visual field, eye-movements are usually classified into catch-up saccades (jumping from one orientation or fixation to another) and smooth pursuit (continuously tracking a target with low velocity). Building on existing dynamic neural field equations, we introduce a novel model that incorporates internal projections to better estimate the current target location (associated to a peak of activity). Such estimate is then used to trigger an eye movement, leading to qualitatively different behaviors depending on the dynamics of the whole oculomotor system: 1) fixational eye-movements due to small variations in the weights of projections when the target is stationary , 2) interceptive and catch-up saccades when peaks build and relax on the neural field, 3) smooth pursuit when the peak stabilizes near the center of the field, the system reaching a fixed point attractor. Learning is nevertheless required for tracking a rapidly moving target , and the proposed model thus replicates recent results in the monkey, in which repeated exercise permits the maintenance of the target within in the central visual field at its current (here-and-now) location, despite the delays involved in transmitting retinal signals to the oculomotor neurons.