  The $\gamma$-ray background from supernovae is calculated on the basis of the
reconstructed efficiency of supernova explosions from star formation at various
redshifts. The calculations presented here show how Type Ia SN rates compatible
with the results of optical supernova searches give a background emission in
the MeV range that can explain the extragalactic emission measured by COMPTEL
and SMM. Star formation histories reaching maximum values of 0.3-0.4
M$_{\odot}$ yr$^{-1}$ Mpc$^{-3}$ at z$\sim$ 1.5 (and/or possibly keeping that
value to higher z) give a $\gamma$-ray background compatible with observations
while they also predict the observed supernova rates per comoving volume. The
$\gamma$-ray background in the MeV range is mostly sensitive to the star
formation rate at z$\sim$ 1-2, but the activity in forming stars at even higher
z has an influence as well on the absolute level of the cosmic $\gamma$-ray
background: the time elapsed by the SNe Ia progenitors until they explode has a
broad distribution and the rates of SNe Ia at z$\sim$ 1.5-2 depend on the
formation frequencies of their progenitor stars at earlier epochs.
  The mutual consistency of predictions of optical rates and integrated
emission in the $\gamma$-ray domain place in a firm ground the Type Ia
supernova identification as the astrophysical source responsible for this
cosmic background
