Can social contextual factors explain international differences in the spread of COVID-19? It is widely assumed that social cohesion, public confidence in government sources of health information and general concern for the welfare of others support health advisories during a pandemic and save lives. We tested this assumption through a time-series analysis of cross-national differences in COVID-19 mortality during an early phase of the pandemic. Country data on income inequality and four dimensions of social capital (trust, group affiliations, civic responsibility and confidence in public institutions) were linked to data on COVID-19 deaths in 84 countries. Associations with deaths were examined using Poisson regression with population-averaged estimators. During a 30-day period after recording their tenth death, mortality was positively related to income inequality, trust and group affiliations and negatively related to social capital from civic engagement and confidence in state institutions. These associations held in bivariate and mutually controlled regression models with controls for population size, age and wealth. The results indicate that societies that are more economically unequal and lack capacity in some dimensions of social capital experienced more COVID-19 deaths. Social trust and belonging to groups were associated with more deaths, possibly due to behavioural contagion and incongruence with physical distancing policy. Some countries require a more robust public health response to contain the spread and impact of COVID-19 due to economic and social divisions within them.