Melanoma, a serious form of skin cancer requires timely and accurate diagnosis to improve the survival rates due to the rapid progression of the disease. Dermoscopic image analysis is a non-invasive procedure for automated melanoma detection but traditional classification methods lack interpretability posing challenges to their adoption in clinical practice and decision-making. This paper presents a novel ensemble framework R-DNet that is developed by integrating better performing deep learning models ResNet-50 and DenseNet for dermoscopic image classification. The proposed approach uses various deep learning models that are fine-tuned with automatically extracted features and the classification performance was evaluated for each model using a wide range of parameters. The classification performance of ResNet-50 is found to be better and this model is ensembled with Inception v3, DenseNet and Xception. The ensembled model R-DNet performs exceptionally well and this model is provided as an input to the explainability framework, Shapley Additive Explanations (SHAP). This framework generates heat maps to detect the critical regions in an image that has the specific characteristics pertaining to the illness. This enables the dermatologists to visualize the significant features and understand the specific patterns and regions for model prediction and classification with enhanced accuracy and explanation. The model performance is evaluated on benchmark dermoscopic dataset, ISIC 2018, demonstrating superior performance in classification accuracy and interpretability. This research work underscores the potential of explainable AI to transform melanoma detection, by aligning the model outputs with dermatological expertise paving way for the physicians to interpret, validate and trust the diagnostic outcomes.