Communicating empathy is important for building relationships in numerous contexts. Consequently, the failure of robots to be perceived as empathetic by human users could be detrimental to developing effective human-robot interaction. Work on computational models of empathy has been growing rapidly, reflecting the importance of this ability for machines. Despite growing recent work, there remain unanswered questions about how users perceive different forms of empathetic expression by robots and how attitudes towards robots may mediate perceptions of robot empathy. Do people really believe that robots can feel or understand emotions? This work studied the difference in viewers' perceptions of cognitive and affective empathetic statements made by a robot in response to hu-man disclosure. In a within-subjects study, participants (n=111) watched videos in which a human disclosed negative emotions around COVID-19, and a robot responded with either affective or cognitive empathetic responses. Using an adapted version of the Robot's Perceived Empathy (RoPE) scale, participants rated their perceptions of the robot's empathy in both cases. We found that participants perceived the robot that made affective empathetic statements as being more empathetic that the robot that made cognitive empathetic statements; we also found that participants with more negative attitudes toward robots were more likely to rate the cognitive condition as more empathetic than the affective condition. These results inform HRI in general and future work into developing robots that will be perceived as empathetic and could personalize empathetic responses to each user.