  The spectrum of an isotropic extragalactic {\gamma}-ray background (EGB) has
been measured by the Fermi-LAT telescope at high latitudes. Two new models for
the EGB are derived from the subraction of unresolved point sources and
extragalactic diffuse processes, which could explain from 30% to 70% of the
Fermi-LAT EGB. Within the hypothesis that the two residual EGBs are entirely
due to the annihilation of dark matter (DM) particles in the Galactic halo, we
obtain stringent upper limits on their annihilation cross section. Severe
bounds on a possible Sommerfeld enhancement of the annihilation cross section
are set as well. Finally, we consider models for DM annihilation depending on
the inverse of the velocity and associate the EGBs to photons arising from the
annihilation of DM in primordial halos. For DM velocities in protohalos of v ~
10^-8 c, the annihilation cross section is constrained down to 10^-33 cm^3 /s
for DM masses below 100 GeV. Given our choices for the EGB and the minimal DM
modelling, the derived upper bounds are claimed to be conservative.
