The commonly used paradigm to investigate Dennet's ‘intentional stance’ compares neural activation when participants compete with a human versus a computer. This paradigm confounds whether the opponent is natural or artificial and whether it is intentional or an automaton. This functional magnetic resonance imaging study is, to our knowledge, the first to investigate the intentional stance by orthogonally varying perceptions of the opponents' intentionality (responding actively or passively according to a script) and embodiment (human or a computer). The mere perception of the opponent (whether human or computer) as intentional activated the mentalizing network: the temporoparietal junction (TPJ) bilaterally, right temporal pole, anterior paracingulate cortex (aPCC) and the precuneus. Interacting with humans versus computers induced activations in a more circumscribed right lateralized subnetwork within the mentalizing network, consisting of the TPJ and the aPCC, possibly reflective of the tendency to spontaneously attribute intentionality to humans. The interaction between intentionality (active versus passive) and opponent (human versus computer) recruited the left frontal pole, possibly in response to violations of the default intentional stance towards humans and computers. Employing an orthogonal design is important to adequately capture Dennett's conception of the intentional stance as a mentalizing strategy that can apply equally well to humans and other intentional agents.