Super-resolution reconstruction (SRR) is a process aimed at enhancing spatial resolution of images, either from a single observation, based on the learned relation between low and high resolution, or from multiple images presenting the same scene. SRR is particularly valuable, if it is infeasible to acquire images at desired resolution, but many images of the same scene are available at lower resolution---this is inherent to a variety of remote sensing scenarios. Recently, we have witnessed substantial improvement in single-image SRR attributed to the use of deep neural networks for learning the relation between low and high resolution. Importantly, deep learning has not been exploited for multiple-image SRR, which benefits from information fusion and in general allows for achieving higher reconstruction accuracy. In this letter, we introduce a new method which combines the advantages of multiple-image fusion with learning the low-to-high resolution mapping using deep networks. The reported experimental results indicate that our algorithm outperforms the state-of-the-art SRR methods, including these that operate from a single image, as well as those that perform multiple-image fusion.