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Rapid assessment after a natural disaster is key for prioritizing emergency resources. In the case of landslides, rapid assessment involves determining the extent of the area affected and measuring the size and location of individual landslides. Synthetic Aperture Radar (SAR) is an active remote sensing technique that is unaffected by weather conditions. Deep Learning algorithms can be applied to SAR data, but training them requires large labeled datasets. In the case of landslides, these datasets are laborious to produce for segmentation, and often they are not available for the specific region in which the event occurred. Here, we study how deep learning algorithms for landslide segmentation on SAR products can benefit from pretraining on a simpler task and from data from different regions. The method we explore consists of two training stages. First, we learn the task of identifying whether a SAR image contains any landslides or not. Then, we learn to segment in a sparsely labeled scenario where half of the data do not contain landslides. We test whether the inclusion of feature embeddings derived from stage-1 helps with landslide detection in stage-2. We find that it leads to minor improvements in the Area Under the Precision-Recall Curve, but also to a significantly lower false positive rate in areas without landslides and an improved estimate of the average number of landslide pixels in a chip. A more accurate pixel count allows to identify the most affected areas with higher confidence. This could be valuable in rapid response scenarios where prioritization of resources at a global scale is important. We make our code publicly available at https://github.com/VMBoehm/SAR-landslide-detection-pretraining.