We present optical identifications for a sample of 20 previously unknown X-ray/radio sources that are present both in the source catalogue of ROSAT PSPC pointed observations (ROSAT SRC) and in the NRAO VLA Sky Survey (NVSS). The optical spectroscopy was carried out with the 2.1-m telescope at San Pedro Martir (Mexico) during 1995 April and September. We have identified 15 active galactic nuclei [including 12 broad-emission-line (FWHM >1000 km s−1) objects, one bona fide BL Lac, one BL Lac candidate and one narrow-line (FWHM < 1000 km s−1) radio galaxy] and five radio galaxies. We derive the X-ray fluxes and luminosities by analysing the PSPC exposures, and show the radio morphology from the NVSS maps. We find that the correlation between the monochromatic X-ray luminosity at 2 keV and the core radio luminosity at 5 GHz for the radio galaxies in our sample follows that found for the 3CR radio galaxies, suggesting a possible nuclear origin for the X-ray emission in these sources. This correlation is weaker in the case of broad-line objects, indicating the presence of another (unbeamed) mechanism for the X-ray emission only weakly related to the radio emission.