Background and Objective: Accurate object segmentation in medical images is a crucial step in medical diagnosis and other applications. Despite years of research on automatic segmentation approaches, achieving clinically acceptable image quality remains challenging. Interactive segmentation is seen as a promising alternative; thus, we propose a new interactive segmentation framework based on a progressive workflow to reduce user effort and provide high-quality results. Method: First, our approach encodes user-provided region clicks and edge scribbles using our proposed disk and curve transform. Then, it is followed by refinement with a transformer-based module that extracts effective features from the outputs of the convolutional neural network (CNN) and the extra input maps. Result: Extensive experiments conducted on various medical images, including ultrasound (US), computerized tomography (CT), and magnetic resonance images (MRI), have demonstrated the effectiveness of our new approach over the state-of-the-art alternatives. Conclusion: The proposed framework can achieve high-quality segmentation using minimal interactions without the substantial cost of manual segmentation.