Medical image classification is critical for clinical decision-making, yet demands for accuracy, interpretability, and generalizability remain challenging. This paper introduces EVM-Fusion, an Explainable Vision Mamba architecture featuring a novel Neural Algorithmic Fusion (NAF) mechanism for multi-organ medical image classification. EVM-Fusion leverages a multipath design, where DenseNet and U-Net based pathways, enhanced by Vision Mamba (Vim) modules, operate in parallel with a traditional feature pathway. These diverse features are dynamically integrated via a two-stage fusion process: cross-modal attention followed by the iterative NAF block, which learns an adaptive fusion algorithm. Intrinsic explainability is embedded through path-specific spatial attention, Vim Δ-value maps, traditional feature SE-attention, and cross-modal attention weights. Experiments on a diverse 9-class multi-organ medical image dataset demonstrate EVM-Fusion's strong classification performance, achieving 99.75% test accuracy and provide multi-faceted insights into its decision-making process, highlighting its potential for trustworthy AI in medical diagnostics.