Accurate building extraction for high-resolution remote sensing images is critical for topographic mapping, urban planning, and many other applications. Its main task is to label each pixel point as a building or non-building. Although deep-learning-based algorithms have significantly enhanced the accuracy of building extraction, fully automated methods for building extraction are limited by the requirement for a large number of annotated samples, resulting in a limited generalization ability, easy misclassification in complex remote sensing images, and higher costs due to the need for a large number of annotated samples. To address these challenges, this paper proposes an improved interactive building extraction model, ARE-Net, which adopts a deep interactive segmentation approach. In this paper, we present several key contributions. Firstly, an adaptive-radius encoding (ARE) module was designed to optimize the interaction features of clicks based on the varying shapes and distributions of buildings to provide maximum a priori information for building extraction. Secondly, a two-stage training strategy was proposed to enhance the convergence speed and efficiency of the segmentation process. Finally, some comprehensive experiments using two models of different sizes (HRNet18s+OCR and HRNet32+OCR) were conducted on the Inria and WHU building datasets. The results showed significant improvements over the current state-of-the-art method in terms of NoC90. The proposed method achieved performance enhancements of 7.98% and 13.03% with HRNet18s+OCR and 7.34% and 15.49% with HRNet32+OCR on the WHU and Inria datasets, respectively. Furthermore, the experiments demonstrated that the proposed ARE-Net method significantly reduced the annotation costs while improving the convergence speed and generalization performance.