Rumor detection on social media platforms is a crucial task for mitigating the spread of misinformation and, sometimes, panic. This study explores an integrated approach for detecting and explaining rumors on social media platforms by leveraging Latent Dirichlet Allocation (LDA) for topic modeling and Local Interpretable Model-agnostic Explanations (LIME) for interpretability or explainability. Finally, a random forest classifier is used to classify the input tweet or message texts into rumor or non-rumor. For this work, we used the publicly available PHEME tweet dataset, which includes binary labels–rumor and non-rumor associated with multiple events. The LDA model effectively identifies latent topics, while the LIME framework clearly explains the basis of the model predictions. Our results demonstrate that this combined methodology provides a robust framework for rumor detection with explainability, achieving a notable accuracy of 0.9213 outperforming similar state-of-the-art systems, and providing valuable insights into decision-making.