Did the COVID-19 pandemic bring people together or push them apart? While infectious diseases tend to push people apart, crises can also bring people together through positive interdependence. We studied this question by asking an international sample (N = 1,006) about their inclinations to cooperate, perceptions of interdependence (i.e., shared fate), and perceived risk as well as local prevalence of COVID-19 infection across 14 time points from March to August, 2020. While perceived interdependence with others tended to increase during this time period, inclinations to cooperate decreased over time. At the within-person level, higher local prevalence of COVID-19 attenuated increases in perceived interdependence with others, and was associated with lower inclinations to cooperate. At the between-person level, people with high perceived interdependence with others reported more stable, or increasing, inclinations to cooperate over time than people with low perceived interdependence. Establishing a high sense of perceived interdependence with others may thus allow people to maintain cooperation during crises, even in the face of challenging circumstances such as those posed by a highly transmissible virus.