Since the end of 2019, the COVID-19 outbreak worldwide has not only presented challenges for government agencies in addressing public health emergency, but also tested their capacity in dealing with public opinion on social media and responding to social emergencies. To understand the impact of COVID-19 related tweets posted by the major public health agencies in the United States on public emotion, this paper studied public emotional diffusion in the tweets network, including its process and characteristics, by taking Twitter users of four official public health systems in the United States as an example. We extracted the interactions between tweets in the COVID-19-TweetIds data set and drew the tweets diffusion network. We proposed a method to measure the characteristics of the emotional diffusion network, with which we analyzed the changes of the public emotional intensity and the proportion of emotional polarity, investigated the emotional influence of key nodes and users, and the emotional diffusion of tweets at different tweeting time, tweet topics and the tweet posting agencies. The results show that the emotional polarity of tweets has changed from negative to positive with the improvement of pandemic management measures. The public's emotional polarity on pandemic related topics tends to be negative, and the emotional intensity of management measures such as pandemic medical services turn from positive to negative to the greatest extent, while the emotional intensity of pandemic related knowledge changes the most. The tweets posted by the Centers for Disease Control and Prevention and the Food and Drug Administration of the United States have a broad impact on public emotions, and the emotional spread of tweets' polarity eventually forms a very close proportion of opposite emotions.