Having conscious experience is arguably the most important reason why it matters to us whether we are alive or dead. A powerful paradigm to identify neural correlates of consciousness is binocular rivalry, wherein a constant visual stimulus evokes a varying conscious percept. It has recently been suggested that activity modulations observed during rivalry may represent the act of report rather than the conscious percept itself. Here, we performed single-unit recordings from face patches in macaque inferotemporal (IT) cortex using a novel no-report paradigm in which the animal’s conscious percept was inferred from eye movements. These experiments reveal two new results concerning the neural correlates of consciousness. First, we found that high proportions of IT neurons represented the conscious percept even without active report. Using high-channel recordings, including a new 128-channel Neuropixels-like probe, we were able to decode the conscious percept on single trials. Second, we found that even on single trials, modulation to rivalrous stimuli was weaker than that to unambiguous stimuli, suggesting that cells may encode not only the conscious percept but also the suppressed stimulus. To test this hypothesis, we varied the identity of the suppressed stimulus during binocular rivalry; we found that indeed, we could decode not only the conscious percept but also the suppressed stimulus from neural activity. Moreover, the same cells that were strongly modulated by the conscious percept also tended to be strongly modulated by the suppressed stimulus. Together, our findings indicate that (1) IT cortex possesses a true neural correlate of consciousness even in the absence of report, and (2) this correlate consists of a population code wherein single cells multiplex representation of the conscious percept and veridical physical stimulus, rather than a subset of cells perfectly reflecting consciousness.