Over recent years, deep convolutional neural networks have significantly advanced the field of face recognition techniques for both verification and identification purposes. Despite the impressive accuracy, these neural networks are often criticized for lacking explainability. There is a growing demand for understanding the decision-making process of AI-based face recognition systems. Some studies have investigated the use of visual saliency maps as explanations, but they have predominantly focused on the specific face verification case. The discussion on more general face recognition scenarios and the corresponding evaluation methodology for these explanations have long been absent in current research. Therefore, this manuscript conceives a comprehensive explanation framework for face recognition tasks. Firstly, an exhaustive definition of visual saliency map-based explanations for AI-based face recognition systems is provided, taking into account the two most common recognition situations individually, i.e., face verification and identification. Secondly, a new model-agnostic explanation method named CorrRISE is proposed to produce saliency maps, which reveal both the similar and dissimilar regions between any given face images. Subsequently, the explanation framework conceives a new evaluation methodology that offers quantitative measurement and comparison of the performance of general visual saliency explanation methods in face recognition. Consequently, extensive experiments are carried out on multiple verification and identification scenarios. The results showcase that CorrRISE generates insightful saliency maps and demonstrates superior performance, particularly in similarity maps in comparison with the state-of-the-art explanation approaches.