Although network address translation (NAT) provides various advantages, it may cause potential threats to network operations. For network administrators to operate networks effectively and securely, it may be necessary to verify whether an assigned IP address is using NAT or not. In this paper, we propose a supervised learning-based active NAT device (NATD) identification using port response patterns. The proposed model utilizes the asymmetric port response patterns between NATD and non-NATD. In addition, to reduce the time and to solve the security issue that supervised learning approaches exhibit, we propose a fast and stealthy NATD identification method. The proposed method can perform the identification remotely, unlike conventional methods that should operate in the same network as the targets. The experimental results demonstrate that the proposed method is effective, exhibiting a F1 score of over 90%. With the efficient features of the proposed methods, we recommend some practical use cases that can contribute to managing networks securely and effectively.