ABSTRACT Using the data of the SRG/eROSITA all-sky survey, we stacked a sample of ∼40 galaxy cluster images in the 0.3–2.3 keV band, covering the radial range up to 10 × R500c. The excess emission on top of the Galactic and extragalactic X-ray backgrounds and foregrounds is detected up to ∼3 × R500c. At these distances, the surface brightness of the stacked image drops below ∼1 per cent of the background. The density profile reconstructed from the X-ray surface brightness profile agrees well (within ∼30 per cent) with the mean gas profile found in numerical simulations, which predict the local gas overdensity of ∼ 20–30 at 3 × R500c and the gas fraction close to the universal value of $\frac{\Omega _b}{\Omega _m}\approx 0.15$ in the standard Λ cold dark matter model. Taking at face value, this agreement suggests that up to ∼3 × R500c the X-ray signal is not strongly boosted by the gas clumpiness, although a scenario with a moderately inhomogeneous gas cannot be excluded. A comparison of the derived gas density profile with the electron pressure profile based on the Sunyaev-Zeldovich (SZ) effect measurements suggests that by r ∼ 3 × R500c the gas temperature drops by a factor of ∼ 4–5 below the characteristic temperature of a typical cluster in the sample within R500c, while the entropy keeps growing up to this distance. Better constraints on the gas properties just beyond 3 × R500c should be possible with a sample larger than used for this pilot study.