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We present two-dimensional gaseous kinematics of the inner 1.2 × 1.8 kpc2 of the Seyfert 2 galaxy NGC 3081, from optical spectra (5600-7000 Å) obtained with the Gemini Multi Object Spectrograph integral field spectrograph on the Gemini North telescope at a spatial resolution of ≈100 pc.We have identified two components in the line emitting gas. A narrower component (full width at half-maximum, FWHM ≈ 60-100 km s-1), which appears to be gas in the galaxy disc, and which shows a distorted rotation pattern, is observed over the whole field of view. A broader component (FWHM ≈ 150-250 km s-1) is present in the inner ≈2 arcsec (200 pc) and shows blueshifts and redshifts in the near and far sides of the galaxy, respectively, consistent with a bipolar outflow. Assuming this to be the case, we estimate that the mass outflow rate in ionized gas(Mout) is between 1.9 ×10-3 and 6.9 ×10-3 M☉ yr-1. The subtraction of a rotation model from the narrower component velocity field reveals a pattern of excess blueshifts of ≈50 km s-1 in the far side of the galaxy and similar excess redshifts in the near side, which are cospatial with a previously known nuclear bar.We interpret these residuals as due to gas following non-circular orbits in the barred potential. Under the assumption that these motions may lead to gas inflows, we estimate an upper limit for the mass inflow rate in ionized gas of ϕ ≈ 1.3 ×10-2 M☉ yr-1. [ABSTRACT FROM AUTHOR]