Rapid mapping of event landslides is crucial to identify the areas affected by damages as well as for effective disaster response. Traditionally, such maps are generated with visual interpretation of remote sensing imagery (manned/unmanned airborne systems or spaceborne sensors) and/or using pixel-based and object-based methods exploiting data-intensive machine learning algorithms. Recent works have explored the use of convolutional neural networks (CNN), a deep learning algorithm, for mapping landslides from remote sensing data. These methods follow a standard supervised learning workflow that involves training a model using a landslide inventory covering a relatively small area. The trained model is then used to predict landslides in the surrounding regions. Here, we propose a new strategy, i.e., a progressive CNN training relying on combined inventories to build a generalized model that can be applied directly to a new, unexplored area. We first prove the effectiveness of CNNs by training and validating on event landslides inventories in four regions after earthquakes and/or extreme meteorological events. Next, we use the trained CNNs to map landslides triggered by new events spread across different geographic regions. We found that CNNs trained on a combination of inventories have a better generalization performance, with a bias towards high precision and low recall scores. In our tests, the combined training model achieved the highest (Matthews correlation coefficient) MCC score of 0.69 when mapping landslides in new unseen regions. The mapping was done on images from different optical sensors, resampled to a spatial resolution of 6 m, 10 m, and 30 m. Despite a slightly reduced performance, the main advantage of combined training is to overcome the requirement of a local inventory for training a new deep learning model. This implementation can facilitate automated pipelines providing fast response for the generation of landslide maps in the post-disaster phase. In this study, the study areas were selected from seismically active zones with a high hydrological hazard distribution and vegetation coverage. Hence, future works should also include regions from less vegetated geographic locations.