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Firms’ public communication on social media during disasters can benefit both disaster response efficiency and the perception of the corporate image. Despite its importance, limited guidelines are available to inform firms’ disaster communication strategies. The current study examines firms’ communication on social media in various disasters and how it impacts public engagement. We employ a novel natural language processing (NLP) approach, Semantic Projection with Active Retrieval (SPAR), to analyze Facebook posts made by Russell 3000 firms between 2009 and 2022 concerning various disasters. We show that firm communication can be measured based on two dimensions derived from the Competing Values Framework (CVF): internal versus external and stable versus flexible. We find that social media messages that emphasize operational continuity (internal/stable-oriented) are more popular during biological disasters. By contrast, messages that stress innovations and adaptations to disasters (external/flexible-oriented) elicit more engagement in weather-related disasters. The study offers a framework to characterize and guide firms’ design of disaster communication on social media in different disaster contexts. Our SPAR method is also available to firms to analyze their social media data and uncover the underlying patterns in communication across different contexts.