Intergenerational interactions between children and older adults are gaining broader recognition because of their mutual benefits. However, such interactions face practical limitations owing to potential disease transmission and the poor health of older adults for face-to-face interactions. This study explores robot-mediated interactions as a potential solution to address these issues. In this study, older adults remotely controlled a social robot to perform a health-screening task for nursery school children, thereby overcoming the problems associated with face-to-face interactions while engaging in physical interactions. The results of this study suggested that the children responded favorably to the robot, and the rate of positive response increased over time. Older adults also found the task generally manageable and experienced a significant positive shift in their attitude toward children. These findings suggest that robot-mediated interactions can effectively facilitate intergenerational engagement and provide psychosocial benefits to both the parties to the engagement. This study provides valuable insights into the potential of robot-mediated interactions in childcare and other similar settings.