We investigated the effect of strategic suppression of reflexive eye movements on external control over fixation using a fixation offset paradigm. A visual signal at fixation facilitates the fixation reflex and inhibits eye movements. Certain preparatory states render the fixation reflex less reactive to visual stimulation at fixation, as evidenced by a reduction in the fixation offset effect (FOE). For example, past studies have suggested that the reduced FOE during anti-saccade tasks results from the requirement to inhibit reflexive eye movements. We tested whether suppressing reflexive saccades reduces external control over ocular fixation using a go-nogo saccade paradigm. During each trial, one of two targets appeared in the periphery. Participants were instructed to saccade to one target (go), but when the other target appeared they either had to maintain fixation (nogo) or move their eyes in the direction opposite the target (anti). When nogo trials were admixed with target-directed saccades a large FOE was observed compared to when target-directed saccades occurred alone (experiment 1); however, when anti-saccades were mixed with target-directed saccades, a small FOE was observed for both types of eye movements (experiment 2). We conclude that suppressing reflexive eye movements does not reduce external control over fixation. Further research is necessary to elucidate which other component of preparing to make an anti-saccade diminishes the FOE.