  We discuss the possibility to observe the products of dark matter
annihilation that was going on in the early Universe. Of all the particles that
could be generated by this process we consider only photons, as they are both
uncharged and easily detectable. The earlier the Universe was, the higher the
dark matter concentration $n$ and the annihilation rate (proportional to $n^2$)
were. However, the emission from the very early Universe cannot reach us
because of the opacity. The main part of the signal was generated at the moment
the Universe had just become transparent for the photons produced by the
annihilation. Thus, the dark matter annihilation in the early Universe should
have created a sort of relic emission. We obtain its flux and the spectrum.
  If weakly interacting massive particles (WIMPs) constitute dark matter, it is
shown that we may expect an extragalactic gamma-ray signal in the energy range
0.5 - 20 {MeV} with a maximum near 8 {MeV}. We show that an experimentally
observed excess in the gamma-ray background at 0.5 - 20 {MeV} could be created
by the relic WIMPs annihilation only if the dark matter structures in the
universe had appeared before the universe became transparent for the
annihilation products ($z \simeq 300$). We discuss in more detail physical
conditions whereby this interpretation could be possible.
