Rising environmental awareness in e-commerce necessitates recommender systems that not only guide users to sustainable products but also minimize their own digital carbon footprints. Traditional session-based systems, optimized for short-term conversions, often fail to capture nuanced user intents for eco-friendly choices, perpetuating a gap between green intentions and actions. To tackle this, we introduce LLMGreenRec, a novel multi-agent framework that leverages Large Language Models (LLMs) to promote sustainable consumption. Through collaborative analysis of user interactions and iterative prompt refinement, LLMGreenRec's specialized agents deduce green-oriented user intents and prioritize eco-friendly product recommendations. Notably, this intent-driven approach also reduces unnecessary interactions and energy consumption. Extensive experiments on benchmark datasets validate LLMGreenRec's effectiveness in recommending sustainable products, demonstrating a robust solution that fosters a responsible digital economy.