With the COVID-19 pandemic, behavioural scientists aimed to illuminate reasons why people comply with (or not) large-scale cooperative activities. Here we investigated the motives that underlie support for COVID-19 preventive behaviours in a sample of 12,758 individuals from 34 countries. We hypothesized that the associations of empathic prosocial concern and fear of disease with support towards preventive COVID-19 behaviours would be moderated by trust in the government. Results suggest that the association between fear of disease and support for COVID-19 preventive behaviours was strongest when trust in the government was weak (both at individual- and country-level). Conversely, the association with empathic prosocial concern was strongest when trust in the government was high, but this moderation was only found at individual-level scores of governmental trust. We discuss how motivations may be shaped by socio-cultural context, and outline how findings may contribute to a better understanding of collective action during global crises.