COVID-19 created significant challenges in crisis management worldwide, especially for local governments that needed to communicate with citizens about health risks, policy decisions, and real-time information related to the pandemic. We analyse the evolution of the engagement between citizens and local governments on Twitter during the different phases of the first wave of the pandemic in Latin America, employing social media intelligence techniques to analyse 106,925 tweets from 103 local governments. Our results show enhanced engagement, especially in participation and collaboration, during the phases studied. Moreover, the increased use of social media as a communication channel was associated with mobility restrictions during the pandemic. Our research contributes to a deeper understanding of the role of social media as a communication channel between governments and citizens in the different phases of crisis management.