For a computer to naturally interact with a human, it needs to be human-like. In this paper, we propose a neural response generation model with multi-task learning of generation and classification, focusing on emotion. Our model based on BART (Lewis et al., 2020), a pre-trained transformer encoder-decoder model, is trained to generate responses and recognize emotions simultaneously. Furthermore, we weight the losses for the tasks to control the update of parameters. Automatic evaluations and crowdsourced manual evaluations show that the proposed model makes generated responses more emotionally aware.