Segmentation of organs or lesions from medical images plays an essential role in many clinical applications such as diagnosis and treatment planning. Though Convolutional Neural Networks (CNN) have achieved the state-of-the-art performance for automatic segmentation, they are often limited by the lack of clinically acceptable accuracy and robustness in complex cases. Therefore, interactive segmentation is a practical alternative to these methods. However, traditional interactive segmentation methods require a large amount of user interactions, and recently proposed CNN-based interactive segmentation methods are limited by poor performance on previously unseen objects. To solve these problems, we propose a novel deep learning-based interactive segmentation method that not only has high efficiency due to only requiring clicks as user inputs but also generalizes well to a range of previously unseen objects. Specifically, we first encode user-provided interior margin points via our proposed exponentialized geodesic distance that enables a CNN to achieve a good initial segmentation result of both previously seen and unseen objects, then we use a novel information fusion method that combines the initial segmentation with only few additional user clicks to efficiently obtain a refined segmentation. We validated our proposed framework through extensive experiments on 2D and 3D medical image segmentation tasks with a wide range of previous unseen objects that were not present in the training set. Experimental results showed that our proposed framework 1) achieves accurate results with fewer user interactions and less time compared with state-of-the-art interactive frameworks and 2) generalizes well to previously unseen objects.