When making a saccadic eye movement to a peripheral target, a simultaneous stimulus onset at central fixation generally increases saccadic latency, while offsets reduce latency ('gap effect'). Visual onsets remote from fixation also increase latency ('remote distractor effect'); however, the influence of remote visual offsets is less clear. Previous studies, which used a search task, found that remote offsets either facilitated, inhibited, or did nothing to saccade latencies towards a peripheral target. It cannot be excluded, however, that the target selection process in such search tasks influenced the results. We therefore simplified the task and asked participants to make eye movements to a predictable target. Simultaneously with target onset, either one or multiple remote stimulus onsets and offsets were presented. It was found that peripheral onsets increased saccade latencies, but offsets did not influence the initiation of a saccade to the target. Moreover, the number of onsets and offsets did not affect the results. These results suggest that earlier effects of remote stimulus offsets and of the number of remote distractor onsets reside in the target identification process of the visual search task rather than the competition between possible saccade goals. The results are discussed in the context of models of saccade target selection.