Many studies have demonstrated that incorporating lexical information into characters can effectively improve the performance of Chinese Named Entity Recognition (CNER). However, we argue that previous studies have not extensively explored the interactive relationship between characters and lexical information, and have only used the lexical information to enhance character-level representation. To address this limitation, we propose an interactive fusion approach that integrates characters and lexical information for CNER. Specifically, we first design graph attention networks to initially fuse character and lexical information within an interactive graph structure. Additionally, by introducing methods such as feedforward neural networks, residual connections, and layer normalization, the fusion effect of the graph attention network is further enhanced. Finally, concatenating and reducing dimensionality of character feature vectors and lexical feature vectors to achieve secondary fusion, thereby obtaining a more comprehensive feature representation. Experimental results on multiple datasets demonstrate that our proposed model outperforms other models that fuse lexical information. Particularly, on the CCKS2020 and Ontonotes datasets, our model achieves higher F1 scores than previous state-of-the-art models. The code is available via the link: https://github.com/wangye0523/The-interactive-fusion-of-characters-and-lexical-information-for-Chinese-named-entity-recognition.