This paper proposes a novel transformer-based framework that aims to enhance weakly supervised semantic segmentation (WSSS) by generating accurate class-specific object localization maps as pseudo labels. Building upon the observation that the attended regions of the one-class token in the standard vision transformer can contribute to a class-agnostic localization map, we explore the potential of the transformer model to capture class-specific attention for class-discriminative object localization by learning multiple class tokens. We introduce a Multi-Class Token transformer, which incorporates multiple class tokens to enable class-aware interactions with the patch tokens. To achieve this, we devise a class-aware training strategy that establishes a one-to-one correspondence between the output class tokens and the ground-truth class labels. Moreover, a Contrastive-Class-Token (CCT) module is proposed to enhance the learning of discriminative class tokens, enabling the model to better capture the unique characteristics and properties of each class. As a result, class-discriminative object localization maps can be effectively generated by leveraging the class-to-patch attentions associated with different class tokens. To further refine these localization maps, we propose the utilization of patch-level pairwise affinity derived from the patch-to-patch transformer attention. Furthermore, the proposed framework seamlessly complements the Class Activation Mapping (CAM) method, resulting in significantly improved WSSS performance on the PASCAL VOC 2012 and MS COCO 2014 datasets. These results underline the importance of the class token for WSSS.