We present the first interferometric observations of CO(1-0) and CO(2-1) line emission from the warped LINER NGC 3718, obtained with the IRAM Plateau de Bure Interferometer (PdBI). This L1.9 galaxy has a prominent dust lane and on kiloparsec scales, a strongly warped atomic and molecular gas disk. The molecular gas is closely associated with the dust lane across the nucleus and its kinematic center is consistent with the millimeter continuum AGN. A comparison of our interferometric mosaic data, which fully cover the ∼9 kpc warped disk, with a previously obtained IRAM 30 m single dish CO(1-0) map shows that the molecular gas distribution in the disk is heavily resolved by the PdBI map. On the nucleus the interferometric maps alone contain less than one half of the single dish line flux, and the overall mosaic accounts for about a tenth of the total molecular gas mass of ∼2.4 × 10 8 M . After applying a short-spacing correction with the IRAM 30 m data to recover the missing extended flux, we find in total six main source components within the dust lane: one associated with the nucleus, four symmetrically positioned on either side at galactocentric distances of about 1.3 kpc and 4.0 kpc from the center, and a sixth on the western side at ∼3 kpc with only a very weak eastern counterpart. In the framework of a kinematic model using tilted rings, we interpret the five symmetric source components as locations of strong orbital crowding. We further find indications that the warp appears not only on kpc scales, but continues down to ∼250 pc. Besides the sixth feature on the western side, the lower flux (a factor of ∼2) of the eastern components compared to the western ones indicates an intrinsic large scale asymmetry in NGC 3718 that cannot be explained by the warp. Indications for a small scale asymmetry are also seen in the central 600 pc. These asymmetries might be evidence for a tidal interaction with a companion galaxy (large scales) and gas accretion onto the nucleus (small scales). Our study of NGC 3718 is part of the NUclei of GAlaxies (NUGA) project that aims at investigating the different processes of gas accretion onto Active Galactic Nuclei (AGN).