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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 <inline-formula><tex-math>$\sim 540$</tex-math></inline-formula>─<inline-formula><tex-math>$720\, \mathrm{km\ s^{-1}}$</tex-math></inline-formula> 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 (<inline-formula><tex-math>$\log \xi \simeq 3.1$</tex-math></inline-formula>) and a low ionization parameter (<inline-formula><tex-math>$\log \xi \simeq 0.36$</tex-math></inline-formula>), 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.