Narrow absorption lines seen in the 2–10 keV spectra of active galaxies and Galactic black holes are normally attributed to iron in high-velocity outflows or inflows. We consider the possibility that such features could arise naturally in the accretion disc. Resonant absorption by highly ionized iron (e.g. Fe xxvi and Fe xxv) in an optically thin plasma that is located above the disc and rotating with it could reproduce narrow features in the reflection component of the spectrum as it emerges from the disc. Depending on the inclination of the disc and the exact geometry of the hot plasma (e.g. whether it blanket the disc or a ring), apparently narrow absorption features could be detected between 4 and 10 keV. Such an explanation requires no high-velocity outflow/inflow and is consistent with a reflection-based interpretation for accreting black holes systems.