Rare diseases pose significant challenges in diagnosis and treatment due to their low prevalence and heterogeneous clinical presentations. Unstructured clinical notes contain valuable information for identifying rare diseases, but manual curation is time-consuming and prone to subjectivity. This study aims to develop a hybrid approach combining dictionary-based natural language processing (NLP) tools with large language models (LLMs) to improve rare disease identification from unstructured clinical reports. We propose a novel hybrid framework that integrates the Orphanet Rare Disease Ontology (ORDO) and the Unified Medical Language System (UMLS) to create a comprehensive rare disease vocabulary. SemEHR, a dictionary-based NLP tool, is employed to extract rare disease mentions from clinical notes. To refine the results and improve accuracy, we leverage various LLMs, including LLaMA3, Phi3-mini, and domain-specific models like OpenBioLLM and BioMistral. Different prompting strategies, such as zero-shot, few-shot, and knowledge-augmented generation, are explored to optimize the LLMs' performance. The proposed hybrid approach demonstrates superior performance compared to traditional NLP systems and standalone LLMs. LLaMA3 and Phi3-mini achieve the highest F1 scores in rare disease identification. Few-shot prompting with 1-3 examples yields the best results, while knowledge-augmented generation shows limited improvement. Notably, the approach uncovers a significant number of potential rare disease cases not documented in structured diagnostic records, highlighting its ability to identify previously unrecognized patients. The hybrid approach combining dictionary-based NLP tools with LLMs shows great promise for improving rare disease identification from unstructured clinical reports. By leveraging the strengths of both techniques, the method demonstrates superior performance and the potential to uncover hidden rare disease cases. Further research is needed to address limitations related to ontology mapping and overlapping case identification, and to integrate the approach into clinical practice for early diagnosis and improved patient outcomes.