Interactive segmentation (IS) using minimal prompts like points and bounding boxes facilitates rapid image annotation, which is crucial for enhancing data-driven deep learning methods. Traditional IS methods, however, process only one target per interaction, leading to inefficiency when annotating multiple identical-class objects in remote sensing imagery (RSI). To address this issue, we present a new task-identical-class object detection (ICOD) for rapid IS in RSI. This task aims to only identify and detect all identical-class targets within an image, guided by a specific category target in the image with its mask. For this task, we propose an ICOD network (ICODet) with a two-stage object detection framework, which consists of a backbone, feature similarity analysis module (S3QFM), and an identical-class object detector. In particular, the S3QFM analyzes feature similarities from images and support objects at both feature-space and semantic levels, generating similarity maps. These maps are processed by a region proposal network (RPN) to extract target-level features, which are then refined through a simple feature comparison module and classified to precisely identify identical-class targets. To evaluate the effectiveness of this method, we construct two datasets for the ICOD task: one containing a diverse set of buildings and another containing multicategory RSI objects. Experimental results show that our method outperforms the compared methods on both datasets. This research introduces a new method for rapid IS of RSI and advances the development of fast interaction modes, offering significant practical value for data production and fundamental applications in the remote sensing community.