To mitigate the impacts and spread of COVID-19, drastic mitigative actions are demanded from individuals worldwide, including social distancing, health behaviors, and self-quarantining. A key question is what motivates individuals to take and support such actions. Early in the COVID-19 crisis, we hypothesized and found in two studies (in the Netherlands and United States) that stronger worries about potential consequences of COVID-19 for oneself and close others (i.e., family and friends), as well as more "distant" others (e.g., citizens in general, vulnerable populations), are associated with stronger engagement in actions to mitigate COVID-19. In line with reasoning on norm activation, we found that these associations were partly mediated by personal norms, reflecting individuals' feelings of being morally compelled and personally responsible to take mitigative actions. Importantly, individuals generally reported to worry more about consequences of COVID-19 for distant others than for themselves, and worries about distant others were more strongly related to mitigative actions than worries about oneself and close others. Our outcomes offer key novel insights to the health domain, highlighting the potential relevance of worrying about distant others and personal norms in motivating actions to mitigate global health crises.