We present soft X-ray spectroscopy of the black-hole X-ray binary V4641 Sgr with the XMM-Newton Reflection Grating Spectrometer (RGS). The RGS spectrum shows narrow emission features from N VI─VII and O VII─VIII superimposed on a partially covered disc blackbody continuum. A blind Gaussian search confirms the presence of significant lines at the expected rest wavelengths. He-like triplet ratios (high G, low R) and full photoionization modelling both indicate a dense, photoionized plasma. Small redshifted velocities of $\sim 540$─$720\, \mathrm{km\ s^{-1}}$ are suggested, which are consistent with quasi-static or slowly flowing gas away from the observer after accounting for systematics. Photoionization modelling requires two XSTAR components with an intermediate ionization parameter ($\log \xi \simeq 3.1$) and a low ionization parameter ($\log \xi \simeq 0.36$), respectively. The simultaneous European Photon Imaging Camera pn (EPIC-pn) spectrum suggests highly ionized Fe emission structures, hinting at an additional, more highly ionized component. These results imply the existence of a radially extended, multiphase, and dense disc atmosphere in the source. We compare the source with other X-ray binaries showing similar emission lines. V4641 Sgr shares a similarly high inclination with other sources; however, the presence of low ionization emission lines distinguishes it from the rest.