  Annihilating dark matter (DM) has been discussed as a possible source of
gamma-rays from the galactic center (GC) and contributing to the extragalactic
gamma-ray background (EGB). Assuming universality of the density profile of DM
halos, we show that it is quite unlikely that DM annihilation is a main
constituent of EGB, without exceeding the observed gamma-ray flux from the GC.
This argument becomes stronger when we include enhancement of the density
profiles by supermassive black holes or baryon cooling. The presence of
substructure may loosen the constraint, but only if a very large cross section
as well as the rather flat profile are realized.
