We present bidimensional spectroscopy of the central region (9."4 x 12."2) of the Seyfert galaxy NGC 3516 in the two spectral ranges 4186-5839 A and 6110-7890 A. The data (95 x 2 spectra) were simultaneously obtained with an optical fibre system (2D-FIS). The two-dimensional velocity map of the stellar component was obtained from the Mg I b absorption lines. The kinematic axes of this stellar velocity field agree very well with the geometrical axes determined from the outer isophotes. In consequence, despite the existence of an outer ring and a bar, the stars in the circumnuclear region rotate regularly. New accurate value for the systemic velocity (2593 +/- 15 km s-1), the orientation of the line of nodes (53 deg +/- 5 deg), and the amplitude of the velocity field (~80 km s-1) are presented. The center of rotation has also been determined and could be spatially displaced with respect to the active nucleus. We have performed an emission-line profile decomposition and identified several components. In addition to the component responsible for the Z-shaped morphology of the line-emission region, gaseous systems showing large widths (FWHM ~ 10-20 A) and extreme blueshift (-900 km s-1) have been found. The comparison between the stellar and ionized-gas velocity maps favors the precessing twin-jet model over the bent-outflow hypothesis to explain the Z-shaped morphology and two-dimensional kinematics of the line-emission region.