Long-range cortico-cortical functional connectivity has long been theorized to be necessary for conscious states. In the present work, we estimate long-range cortical connectivity in a series of intracranial and scalp EEG recordings experiments. In the two first experiments intracranial-EEG (iEEG) was recorded during four distinct states within the same individuals: conscious wakefulness (CW), rapid-eye-movement sleep (REM), stable periods of slow-wave sleep (SWS) and deep propofol anaesthesia (PA). We estimated functional connectivity using the following two methods: weighted Symbolic-Mutual-Information (wSMI) and phase-locked value (PLV). Our results showed that long-range functional connectivity in the delta-theta frequency band specifically discriminated CW and REM from SWS and PA. In the third experiment, we generalized this original finding on a large cohort of brain-injured patients. FC in the delta-theta band was significantly higher in patients being in a minimally conscious state (MCS) than in those being in a vegetative state (or unresponsive wakefulness syndrome). Taken together the present results suggest that FC of cortical activity in this slow frequency band is a new and robust signature of conscious states.