Manual diagnosis of skin cancer is time-consuming and expensive; therefore, it is essential to develop automated diagnostics methods with the ability to classify multiclass skin lesions with greater accuracy. We propose a fully automated approach for multiclass skin lesion segmentation and classification by using the most discriminant deep features. First, the input images are initially enhanced using local color-controlled histogram intensity values (LCcHIV). Next, saliency is estimated using a novel Deep Saliency Segmentation method, which uses a custom convolutional neural network (CNN) of ten layers. The generated heat map is converted into a binary image using a thresholding function. Next, the segmented color lesion images are used for feature extraction by a deep pre-trained CNN model. To avoid the curse of dimensionality, we implement an improved moth flame optimization (IMFO) algorithm to select the most discriminant features. The resultant features are fused using a multiset maximum correlation analysis (MMCA) and classified using the Kernel Extreme Learning Machine (KELM) classifier. The segmentation performance of the proposed methodology is analyzed on ISBI 2016, ISBI 2017, ISIC 2018, and PH2 datasets, achieving an accuracy of 95.38%, 95.79%, 92.69%, and 98.70%, respectively. The classification performance is evaluated on the HAM10000 dataset and achieved an accuracy of 90.67%. To prove the effectiveness of the proposed methods, we present a comparison with the state-of-the-art techniques.