Background Public engagement is a key element for mitigating pandemics, and a good understanding of public opinion could help to encourage the successful adoption of public health measures by the population. In past years, deep learning has been increasingly applied to the analysis of text from social networks. However, most of the developed approaches can only capture topics or sentiments alone but not both together. Objective Here, we aimed to develop a new approach, based on deep neural networks, for simultaneously capturing public topics and sentiments and applied it to tweets sent just after the announcement of the COVID-19 pandemic by the World Health Organization (WHO). Methods A total of 1,386,496 tweets were collected, preprocessed, and split with a ratio of 80:20 into training and validation sets, respectively. We combined lexicons and convolutional neural networks to improve sentiment prediction. The trained model achieved an overall accuracy of 81% and a precision of 82% and was able to capture simultaneously the weighted words associated with a predicted sentiment intensity score. These outputs were then visualized via an interactive and customizable web interface based on a word cloud representation. Using word cloud analysis, we captured the main topics for extreme positive and negative sentiment intensity scores. Results In reaction to the announcement of the pandemic by the WHO, 6 negative and 5 positive topics were discussed on Twitter. Twitter users seemed to be worried about the international situation, economic consequences, and medical situation. Conversely, they seemed to be satisfied with the commitment of medical and social workers and with the collaboration between people. Conclusions We propose a new method based on deep neural networks for simultaneously extracting public topics and sentiments from tweets. This method could be helpful for monitoring public opinion during crises such as pandemics.