  We study the origin of the extragalactic diffuse gamma-ray background using
the data from the Fermi telescope. To estimate the background level, we count
photons at high Galactic latitudes |b|>60 degrees. Subtracting photons
associated to known sources and the residual cosmic ray and Galactic diffuse
backgrounds, we estimate the Extragalactic Gamma-ray Background (EGB) flux. We
find that the spectrum of EGB in the very-high-energy (VHE) band above 30 GeV
follows the stacked spectrum of BL Lacs. LAT data reveal the positive (1+z)^k,
1<k<4 cosmological evolution of the BL Lac source population consistent with
that of their parent population, FR I radio galaxies. We show that EGB at E>30
GeV could be completely explained by emission from unresolved BL Lacs if k~3.
