The early and accurate classification of skin lesions are crucial, enabling dermatologists to provide timely and effective treatment, ultimately saving lives. A computer diagnostic system that utilizes deep learning (DL) offers an effective automated solution for clinical evaluations. Convolutional neural networks (CNNs) can significantly improve the accuracy at which skin lesions are classified from dermoscopic images, obviating the necessity for human intervention. In this context, we have modified a pre-trained NasNetMobile architecture and fine-tuned it on skin lesion images. Additional layers are included into the actual NasNetMobile architecture to enhance the discriminating accuracy and improve the feature extraction robustness. A multi-class support vector machine classifier is subsequently trained using the features extracted from the modified architecture. To test the effectiveness of this approach, we conducted experiments on challenging ISIC 2018 dataset. The incorporation of a new set of layers enhances the categorization performance of the proposed modified NasNetMobile approach, surpassing both the simple fine-tuning of NasNetMobile and numerous other existing techniques, achieving an impressive mean diagnostic accuracy of 95.85% in categorizing skin lesions.