I use ASCA data to investigate the 2–10 keV X‐ray emission of active galactic nuclei (AGN) taken from the ROSAT International X‐ray Optical Survey (RIXOS). I find that the integrated spectrum of these faint, soft X‐ray‐selected AGN in the 2–10 keV band is harder (best‐fitting α = 0.8 ± 0.1) than the slope measured with ROSAT between 0.1 and 2 keV, but softer than the 2–10 keV X‐ray background, and consistent with the average 2–10 keV spectrum of bright, nearby Seyfert galaxies. With this spectral slope and using measurements of the AGN contribution to the 1–2 keV X‐ray background, I estimate that the AGN percentage contribution to the 2–10 keV background is 0.60 +0.19−0.14 times the AGN percentage contribution to the 1–2 keV background. Hence AGN produce between 12 and 32 per cent of the 2–10 keV X‐ray background. This is only the contribution from the types of AGN which are found in soft X‐ray surveys; a population of absorbed AGN could represent an additional component of the 2–10 keV X‐ray background.