Knowing how people perceive multiple risks is essential to the management and promotion of public health and safety. Here we present a dataset based on a survey (N = 4,154) of public risk perception in Italy and Sweden during the COVID-19 pandemic. Both countries were heavily affected by the first wave of infections in Spring 2020, but their governmental responses were very different. As such, the dataset offers unique opportunities to investigate the role of governmental responses in shaping public risk perception. In addition to epidemics, the survey considered indirect effects of COVID-19 (domestic violence, economic crises), as well as global (climate change) and local (wildfires, floods, droughts, earthquakes, terror attacks) threats. The survey examines perceived likelihoods and impacts, individual and authorities' preparedness and knowledge, and socio-demographic indicators. Hence, the resulting dataset has the potential to enable a plethora of analyses on social, cultural and institutional factors influencing the way in which people perceive risk.