Medical dialogue generation (MDG) has gained increasing attention due to its substantial practical value. Previous works typically employ a sequence-to-sequence framework to generate medical responses by modeling dialogue context as sequential text with annotated medical entities. While these methods have been successful in generating fluent responses, they fail to provide process explanations of reasoning and require extensive entity annotation. To address these limitations, we propose the method Bootstrap Prompting for Explicit Reasoning in MDG (BP4ER), which explicitly model MDG’s multi-step reasoning process and iteratively enhance this reasoning process. We employ a least-to-most prompting strategy to guide a large language model (LLM) in explicit reasoning, breaking down MDG into simpler sub-questions. These sub-questions build on answers from previous ones. Additionally, we also introduce two distinct bootstrapping techniques for prompting, which autonomously correct errors and facilitate the LLM’s explicit reasoning. This approach eliminates the need for entity annotation and increases the transparency of the MDG process by explicitly generating the intermediate reasoning chain. Experimental results on the two publicly datasets show that BP4ER outperforms state-of-the-art methods across both objective and subjective evaluation.