We present emission-line flux distributions and ratios for the inner ≈ 200 pc of the narrow-line region of the Seyfert 2 galaxy NGC 1068, using observations obtained with the Gemini Near-infrared Integral Field Spectrograph (NIFS) in the J, H and K bands at a spatial resolution of ≈ 10 pc and spectral resolution of ≈ 5300. The molecular gas emission -traced by the K-band H 2 emission lines -outlines an offcentered circumnuclear ring with a radius of ≈ 100 pc showing thermal excitation. The ionized gas emission lines show flux distributions mostly outlining the previously known [O iii]λ5007 ionization bicone. But while the flux distributions in the H i and He ii emission lines are very similar to that observed in [O iii], the flux distribution in the [Fe ii] emission lines is more extended and broader than a cone close to the nucleus, showing a "double bowl" or 'hourglass" structure". This difference is attributed to the fact that the [Fe ii] emission, besides coming from the fully ionized region, comes also from the more extended partially ionized regions, in gas excited mainly by X-rays from the active galactic nucleus. A contribution to the [Fe ii] emission from shocks along the bicone axis to NE and SW of the nucleus is also supported by the enhancement of the [Fe ii](1.2570 µm)/[P ii](1.1885 µm) and [Fe ii](1.2570 µm)/Paβ emission-line ratios at these locations and is attributed to the interaction of the radio jet with the NLR. The mass of ionized gas in the inner 200 pc of NGC 1068 is M H II ≈ 2.2 × 10 4 M , while the mass of the H 2 emitting gas is only M H2 ≈ 29 M . Taking into account the dominant contribution of the cold molecular gas, we obtain an estimate of the total molecular gas mass of M cold ≈ 2 × 10 7 M .