  The contribution of Source Cosmic Rays (SCRs), accelerated and still confined
in Supernova Remnants (SNRs), to the diffuse high energy \gr emission above 1
GeV from the Galactic disk is studied. The \grs produced by the SCRs have a
much harder spectrum than those generated by the Galactic Cosmic Rays (GCRs).
Extending a previous paper, a simple SNR population synthesis is considered and
the Inverse Compton emission from the SCR electrons is evaluated in greater
detail. Then the combined spectrum of \gr emission from the Galactic Supernova
Remnant population is calculated and this emission at low Galactic latitudes is
compared with the diffuse \gr emission observed by the EGRET and ground based
instruments. The average contribution of SCRs is comparable to the GCR
contribution already at GeV energies, due to Supernovae of types II and Ib
exploding into the wind bubbles of quite massive progenitor stars, and becomes
dominant at \gr energies above 100 GeV. At TeV energies the dominant
contribution is from SCRs in SNRs that expand into a uniform interstellar
medium. In fact, the sum of hadronic and Inverse Compton \grs would exceed the
limits given by the existing experimental data, unless the confinement time
$T_{SN}$, i.e. the time until which SNRs confine the main fraction of
accelerated SCRs, is as small as $T_{SN}\sim 10^4$ yr and the typical magnetic
field strength in SNRs as large as 30 $\mu$G. Both situations are however
possible as a result of field amplification through CR backreaction in the
acceleration process. It is pointed out that accurate measurements of the
low-latitude diffuse Galactic \gr spectrum at TeV-energies can serve as a
unique consistency test for CR origin from the Supernova Remnant population as
a whole.
