  The origin of the diffuse gamma-ray background in the range from hundreds keV
to several MeV is not known conclusively. From current models and observations
it is believed that, at least partially, this background is formed by blazars
and remnants of supernovae (SN) of type Ia in distant galaxies. However, these
contributions are not sufficient to reproduce the observed level of the signal.
In this work we propose another source which could contribute to this
background, namely the jets of active galactic nuclei (AGN). The composition of
jets is not known, but there are observational hints that the fraction of
positrons there is substantial. Positrons are partially evacuated to the
intergalactic medium and partially mix with the circumgalactic medium and
annihilate there comparatively quickly. Using the AGN luminosity function, we
estimated the positron production rate and the contribution of the positron
annihilation to the cosmic background below 511 keV. We also estimated the
analogous contribution from positron annihilation within SN Ia remnants in
distant galaxies. The contribution of AGNs is estimated to be a factor of 5 -
10 smaller than the observed background intensity, and the contribution from
SNe is yet smaller by one order of magnitude. Nevertheless, the contribution of
AGNs appeared to be larger than the contribution of blazars estimated from
Swift-BAT and Fermi-LAT observations. The main uncertainty in our model is the
fraction of positrons remaining in the circumgalactic medium which makes our
estimation an upper limit.
