We present a new spectroscopic study of the faint Milky Way satellite Sagittarius II. Using multiobject spectroscopy from the Fibre Large Array Multi-Element Spectrograph, we supplement the data set of Longeard et al. with 47 newly observed stars, 19 of which are identified as members of the satellite. These additional member stars are used to put tighter constraints on the dynamics and the metallicity properties of the system. We find a low velocity dispersion of $\sigma _\mathrm{v}^\mathrm{SgrII} = 1.7 \pm 0.5$ km s-1, in agreement with the dispersion of Milky Way globular clusters of similar luminosity. We confirm the very metal-poor nature of the satellite ([Fe/H] $_\mathrm{spectro}^\mathrm{SgrII} = -2.23 \pm 0.07$ ) and find that the metallicity dispersion of Sgr II is not resolved, reaching only 0.20 at the 95 per cent confidence limit. No star with a metallicity below -2.5 is confidently detected. Therefore, despite the unusually large size of the system (r $_h = 35.5 ^{+1.4}_{-1.2}$ pc), we conclude that Sgr II is an old and metal-poor globular cluster of the Milky Way.