The ability to constructively resolve interpersonal conflicts is a crucial set of social skills people need to effectively work and live well together. Is it possible to design social robots to support the early development of children's interpersonal conflict resolution skills? To investigate this question, 64 (32 pairs of) children ages 3-6 years engaged in a 50-minute play session consisting of 5 activities facilitated by the robot Keepon. Children were randomly assigned to 1 of 2 conditions. In the mediation condition, Keepon directed the play session flow by indicating when and which activity to switch to, and whenever possible, signaled the onset of object possession conflicts that occurred between the pair and offered prompts for constructive conflict resolution. In the control condition, Keepon only facilitated and directed the play session and did not intervene during children's conflicts. Results show that children were more likely to resolve conflicts constructively in the mediation condition than in the control condition, and that a key function for a robot mediator within the conflict process is to successfully flag the conflict onset. Drawing from these findings, we discuss design recommendation for a robot mediator.