Abstract: 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 subtraction 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. Given our choices for the EGB and the minimal DM modeling, the derived upper bounds are claimed to be conservative.