With advances in technology, artificial agents such as humanoid robots will soon become a part of our daily lives. For safe and intuitive collaboration, it is important to understand the goals behind their motor actions. In humans, this process is mediated by changes in activity in fronto-parietal brain areas. The extent to which these areas are activated when observing artificial agents indicates the naturalness and easiness of interaction. Previous studies indicated that fronto-parietal activity does not depend on whether the agent is human or artificial. However, it is unknown whether this activity is modulated by observing grasping (self-related action) and pointing actions (other-related action) performed by an artificial agent depending on the action goal. Therefore, we designed an experiment in which subjects observed human and artificial agents perform pointing and grasping actions aimed at two different object categories suggesting different goals. We found a signal increase in the bilateral inferior parietal lobule and the premotor cortex when tool versus food items were pointed to or grasped by both agents, probably reflecting the association of hand actions with the functional use of tools. Our results show that goal attribution engages the fronto-parietal network not only for observing a human but also a robotic agent for both self-related and social actions. The debriefing after the experiment has shown that actions of human-like artificial agents can be perceived as being goal-directed. Therefore, humans will be able to interact with service robots intuitively in various domains such as education, healthcare, public service, and entertainment.