The rising demand for mental health care has fueled interest in AI-driven counseling systems. While large language models (LLMs) offer significant potential, current approaches face challenges, including limited understanding of clients' psychological states and counseling stages, reliance on high-quality training data, and privacy concerns associated with commercial deployment. To address these issues, we propose EmoStage, a framework that enhances empathetic response generation by leveraging the inference capabilities of open-source LLMs without additional training data. Our framework introduces perspective-taking to infer clients' psychological states and support needs, enabling the generation of emotionally resonant responses. In addition, phase recognition is incorporated to ensure alignment with the counseling process and to prevent contextually inappropriate or inopportune responses. Experiments conducted in both Japanese and Chinese counseling settings demonstrate that EmoStage improves the quality of responses generated by base models and performs competitively with data-driven methods.