Text classification aims to effectively categorize documents into pre-defined categories. Traditional methods for text classification often rely on large amounts of manually annotated training data, making the process time-consuming and labor-intensive. To address this issue, recent studies have focused on weakly-supervised and extremely weakly-supervised settings, which require minimal or no human annotation, respectively. In previous methods of weakly supervised text classification, pseudo-training data is generated by assigning pseudo-labels to documents based on their alignment (e.g., keyword matching) with specific classes. However, these methods ignore the importance of incorporating the explanations of the generated pseudo-labels, or saliency of individual words, as additional guidance during the text classification training process. To address this limitation, we propose XAI-CLASS, a novel explanation-enhanced extremely weakly-supervised text classification method that incorporates word saliency prediction as an auxiliary task. XAI-CLASS begins by employing a multi-round question-answering process to generate pseudo-training data that promotes the mutual enhancement of class labels and corresponding explanation word generation. This pseudo-training data is then used to train a multi-task framework that simultaneously learns both text classification and word saliency prediction. Extensive experiments on several weakly-supervised text classification datasets show that XAI-CLASS outperforms other weakly-supervised text classification methods significantly. Moreover, experiments demonstrate that XAI-CLASS enhances both model performance and explainability.