The merger remnant NGC 1316 (Fornax A) is one of the most important objects regarding the investigation of merger-related processes. We use kinematical data of globular clusters (GCs) and the diffuse stellar light to investigate the global structure of NGC 1316 and to constrain the dark matter content. We perform multi-object-spectroscopy with VLT/FORS2 and MXU. Out of 562 slits, we extract radial velocities for 177 GCs. Moreover, we measure radial velocities of the integrated galaxy light, using slits with a sufficiently bright sky. To these data, we add 20 cluster velocities from Goudfrooij et al. (2001). In an appendix, we identify new morphological features of NGC 1316 and its companion galaxy NGC 1317. The GC sample based on radial velocities confirms the colour peaks already found in our photometric study. The bright clusters, which probably have their origin in a 2 Gyr-old starburst and younger star formation events, avoid the systemic velocity. A Gaussian velocity distribution is found only for clusters fainter than about m_R=22 mag. The velocity distribution of clusters shows a pronounced peak at 1600 km/s. These clusters populate a wide area in the south-western region which we suspect to be a disk population. Globular clusters or subsamples of them do not show a clear rotation signal. This is different from the galaxy light, where rotation along the major axis is discernable out to 3 arcmin radius. A simple spherical model like that suggested by dynamical analyses of planetary nebulae reproduces also the velocity dispersions of the faint GCs. The central dark matter density of the present model resembles a giant elliptical galaxy. This contradicts population properties which indicate spiral galaxies as pre-merger components. MOND would provide a solution, but the kinematical complexity of NGC 1316 does not allow a really firm conclusion. (abridged)
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