Training a computer vision system to segment a novel class typically requires collecting and painstakingly annotating lots of images with objects from that class. Few-shot segmentation techniques reduce the required number of images to learn to segment a new class, but careful annotations of object boundaries are still required. On the other hand, interactive segmentation techniques only focus on incrementally improving the segmentation of one object at a time (typically, using clicks given by an expert) in a class-agnostic manner. We combine the two concepts to drastically reduce the effort required to train segmentation models for novel classes. Instead of trivially feeding interactive segmentation masks as ground truth to a few-shot segmentation model, we propose IFSENet, which can accept sparse supervision on a single or few support images in the form of clicks to generate masks on support (training, at least clicked upon once) as well as query (test, never clicked upon) images. To trade-off effort for accuracy flexibly, the number of images and clicks can be incrementally added to the support set to further improve the segmentation of support as well as query images. The proposed model approaches the accuracy of previous state-of-the-art few-shot segmentation models with considerably lower annotation effort (clicks instead of maps), when tested on Pascal and SBD datasets on query images. It also works well as an interactive segmentation method on support images.