The Coronavirus pandemic poses a major health and economic threat to societies around the world. The success of new measures that policymakers and health officials have introduced to combat the pandemic often relies on voluntary compliance by citizens. While the pandemic has brought increased relevance to altruistic and prosocial behavior, it is unclear if the pandemic coincides with changes in self-reported dispositional empathy, and to what extent dispositional empathy affects support for governmental measures. I use a large two-wave panel survey of UK citizens (N=7480) to analyze (1) if the Coronavirus pandemic led to an increase in affective and cognitive empathy from pre- to mid-pandemic, and (2) in what way affective and cognitive empathy drive support for ten governmental measures to combat the pandemic, such as hand washing, mask wearing, social distancing and fining rule-breakers, conditional on perceived threat to health and the economy. I find that affective and cognitive empathy remained stable from pre- to mid-pandemic on average, but that there are significant differences between demographic groups. Dispositional empathy generally predicts stronger support for measures to combat the pandemic, but there are significant differences between different types of measures, and support is highly conditional on perceived health and economic threat.