Common object counting in a natural scene is a challenging problem in computer vision with numerous real-world applications. Existing image-level supervised common object counting approaches only predict the global object count and rely on additional instance-level supervision to also determine object locations. We propose an image-level supervised approach that provides both the global object count and the spatial distribution of object instances by constructing an object category density map. Motivated by psychological studies, we further reduce image-level supervision using a limited object count information (up to four). To the best of our knowledge, we are the first to propose image-level supervised density map estimation for common object counting and demonstrate its effectiveness in image-level supervised instance segmentation. Comprehensive experiments are performed on the PASCAL VOC and COCO datasets. Our approach outperforms existing methods, including those using instance-level supervision, on both datasets for common object counting. Moreover, our approach improves state-of-the-art image-level supervised instance segmentation [34] with a relative gain of 17.8% in terms of average best overlap, on the PASCAL VOC 2012 dataset.