We present new interferometer observations of the ¹²CO (1-0) and ¹²CO (2-1) line emission of NGC 1068 with a resolution of 07. The molecular gas in the inner 5'' is resolved into a ring with two bright knots east and west of the nuclear continuum emission. For the first time in NGC 1068, we can trace molecular gas at ≈018 (13 pc) from the nucleus. The high velocities in this region imply an enclosed mass of ~10⁸ M. This value is consistent with a black hole mass of 1.7 × 10⁷ M, as estimated from nuclear H₂O maser emission, plus a contribution from a compact nuclear stellar cluster. Perpendicular to the kinematic major axis, optical images of NGC 1068 show a bright, stellar, oval structure of eccentricity 0.8 and a deprojected length of 17 kpc. Analysis of the rotation curve shows the CO spiral arms are at the inner Lindblad resonance of this barlike structure. Inside the molecular spiral arms, 10'' from the nucleus, the CO kinematic axis changes direction probably in response to the 2.5 kpc (deprojected) long stellar bar seen in the near-infrared (NIR). The low velocity dispersion indicates the molecular gas is in a disk with a thickness of 10 pc in the nuclear region and 100 pc in the spiral arms.

We constructed kinematic models for the molecular gas using elliptical orbits caused by a ~1'' (72 pc) nuclear bar and using tilted rings resulting in a warp. We find that the gas motions are consistent with either the warp or the bar models. However, because there is no evidence for a ~1'' nuclear bar in NIR images, we favor the warp model. A warped CO disk can also explain the obscuration of the active galactic nucleus (AGN), the extinction of light from the nuclear stellar cluster, and the observed NIR and mid-IR polarization. The model predicts that the warped CO disk should become edge-on at a radius of 70 pc, thereby creating a cavity for the ionization cone.