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Medical coding is essential for standardizing clinical data and communication but is often time-consuming and prone to errors. Traditional Natural Language Processing (NLP) methods struggle with automating coding due to the large label space, lengthy text inputs, and the absence of supporting evidence annotations that justify code selection. Recent advancements in Generative Artificial Intelligence (AI) offer promising solutions to these challenges. In this work, we introduce MedCodER, a Generative AI framework for automatic medical coding that leverages extraction, retrieval, and re-ranking techniques as core components. MedCodER achieves a micro-F1 score of 0.60 on International Classification of Diseases (ICD) code prediction, significantly outperforming state-of-the-art methods. Additionally, we present a new dataset containing medical records annotated with disease diagnoses, ICD codes, and supporting evidence texts (https://doi.org/10.5281/zenodo.13308316). Ablation tests confirm that MedCodER's performance depends on the integration of each of its aforementioned components, as performance declines when these components are evaluated in isolation.