Background The effective implementation of government policies and measures for controlling the coronavirus disease 2019 (COVID-19) pandemic requires compliance from the public. This study aimed to examine cross-sectional and longitudinal associations of trust in government regarding COVID-19 control with the adoption of recommended health behaviours and prosocial behaviours, and potential determinants of trust in government during the pandemic. Methods This study analysed data from the PsyCorona Survey, an international project on COVID-19 that included 23 733 participants from 23 countries (representative in age and gender distributions by country) at baseline survey and 7785 participants who also completed follow-up surveys. Specification curve analysis was used to examine concurrent associations between trust in government and self-reported behaviours. We further used structural equation model to explore potential determinants of trust in government. Multilevel linear regressions were used to examine associations between baseline trust and longitudinal behavioural changes. Results Higher trust in government regarding COVID-19 control was significantly associated with higher adoption of health behaviours (handwashing, avoiding crowded space, self-quarantine) and prosocial behaviours in specification curve analyses (median standardised β = 0.173 and 0.229, p < 0.001). Government perceived as well organised, disseminating clear messages and knowledge on COVID-19, and perceived fairness were positively associated with trust in government (standardised β = 0.358, 0.230, 0.056, and 0.249, p < 0.01). Higher trust at baseline survey was significantly associated with lower rate of decline in health behaviours over time (p for interaction = 0.001). Conclusions These results highlighted the importance of trust in government in the control of COVID-19.