Functional connectivity of neural oscillations (oscillation-based FC) is thought to afford dynamic information exchange across task-relevant neural ensembles. Although oscillation-based FC is classically defined relative to a prestimulus baseline, giving rise to rapid, context-dependent changes in individual connections, studies of distributed spatial patterns show that oscillation-based FC is omnipresent, occurring even in the absence of explicit cognitive demands. Thus, the issue of whether oscillation-based FC is primarily shaped by cognitive state or is intrinsic in nature remains open. Accordingly, we sought to reconcile these observations by interrogating the ECoG recordings of 18 presurgical human patients (8 females) for state dependence of oscillation-based FC in five canonical frequency bands across an array of six task states. FC analysis of phase and amplitude coupling revealed a highly similar, largely state-invariant (i.e., intrinsic) spatial component across cognitive states. This spatial organization was shared across all frequency bands. Crucially, however, each band also exhibited temporally independent FC dynamics capable of supporting frequency-specific information exchange. In conclusion, the spatial organization of oscillation-based FC is largely stable over cognitive states (i.e., primarily intrinsic in nature) and shared across frequency bands. Together, our findings converge with previous observations of spatially invariant patterns of FC derived from extremely slow and aperiodic fluctuations in fMRI signals. Our observations indicate that "background" FC should be accounted for in conceptual frameworks of oscillation-based FC targeting task-related changes. A fundamental property of neural activity is that it is periodic, enabling functional connectivity (FC) between distant regions through coupling of their oscillations. According to task-based studies, such oscillation-based FC is rapid and malleable to meet cognitive task demands. Studying distributed FC patterns instead of FC in a few individual connections, we found that oscillation-based FC is largely stable across various cognitive states and shares a common layout across oscillation frequencies. This stable spatial organization of FC in fast oscillatory brain signals parallels the known stability of fMRI-based intrinsic FC architecture. Despite the observed spatial state and frequency invariance, FC of individual connections was temporally independent between frequency bands, suggesting a putative mechanism for malleable frequency-specific FC to support cognitive tasks.