While the epidemic of SARS-CoV-2 has spread worldwide, there is much concern over the mortality rate that the infection induces. Available data suggest that COVID-19 case fatality rate had varied temporally (as the epidemic has progressed) and spatially (among countries). Here, we attempted to identify key factors possibly explaining the variability in case fatality rate across countries. We used data on the temporal trajectory of case fatality rate provided by the European Center for Disease Prevention and Control, and country-specific data on different metrics describing the incidence of known comorbidity factors associated with an increased risk of COVID-19 mortality at the individual level. We also compiled data on demography, economy and political regimes for each country. We found that temporal trajectories of case fatality rate greatly vary among countries. We found several factors associated with temporal changes in case fatality rate both among variables describing comorbidity risk and demographic, economic and political variables. In particular, countries with the highest values of DALYs lost to cardiovascular, cancer and chronic respiratory diseases had the highest values of COVID-19 CFR. CFR was also positively associated with the death rate due to smoking in people over 70 years. Interestingly, CFR was negatively associated with share of death due to lower respiratory infections. Among the demographic, economic and political variables, CFR was positively associated with share of the population over 70, GDP per capita, and level of democracy, while it was negatively associated with number of hospital beds ×1000. Overall, these results emphasize the role of comorbidity and socio-economic factors as possible drivers of COVID-19 case fatality rate at the population level.