We map the kinematics of the inner (200 pc) narrow-line region (NLR) of the Seyfert 2 galaxy NGC 1068 using the instrument Near-infrared Integral Field Spectrograph and adaptive optics at the Gemini North telescope. Channel maps and position–velocity diagrams are presented at a spatial resolution of ∼= 8 pc and spectral resolution ∼5300 in the emission lines [Fe II] λ1.644 μm, H2 λ2.122 μm and Brγ. The [Fe II] emission line provides a better coverage of the NLR outflow than the previously used [O III] λ5007 emission line, extending beyond the area of the bipolar cone observed in Brγ and [O III]. This is mainly due to the contribution of the redshifted channels to the north-east of the nucleus, supporting its origin in a partial ionized zone with additional contribution from shocks of the outflowing gas with the galactic disc. We modelled the kinematics and geometry of the [Fe II] emitting gas finding good agreement with the data for outflow models with conical and lemniscate (or hourglass) geometry.We calculate a mass outflow rate of 1.9+2 −1 M yr−1 but a power for the outflow of only 0.08 per cent LBol. The molecular (H2) gas kinematics is completely distinct from that of [Fe II] and Brγ , showing radial expansion in an off-centred ∼100 pc radius ring in the galaxy plane. The expansion velocity decelerates from ≈200 km s−1 in the inner border of the ring to approximately zero at the outer border where our previous studies found a 10 Myr stellar population