When bright moving objects are viewed with an electro-optical system at long range, they appear as small, slightly blurred moving points in the recorded image sequence. Typically, such point targets need to be detected in an early stage. However, in some scenarios the background of a scene may contain much structure, which makes it difficult to detect a point target. The novelty of this work is that superresolution reconstruction is used for suppression of the background. With superresolution reconstruction a high-resolution estimate of the background, without aliasing artifacts due to undersampling, is obtained. After applying a camera model and subtraction, this will result in difference images containing only the point target and temporal noise. In our experiments, based on realistic scenarios, the detection performance, after background suppression using superresolution reconstruction, is compared with the detection performance of a common background suppression method. It is shown that using the proposed method, for an equal detection-to-false-alarm ratio, the signal strength of a point target can be up to 4 times smaller. This implies that a point target can be detected at a longer range.