  We consider the emission within the fireball model framework of very high
energy, ~1 GeV to >1 TeV photons, on a minute time scale, during the onset of
fireball deceleration due to interaction with surrounding medium. Our time
dependent numerical model includes exact treatment of electron synchrotron
emission, inverse-Compton scattering, pair production, and evolution of
electromagnetic cascades (initiated by pair production or photo-production of
pions). We find that (i) The 1 GeV--10 GeV flux is not sensitive to model
parameters and is ~10^{-7} erg cm^-2 s^-1 for z=1 bursts, well within the
detection capabilities of GLAST; (ii) The sub-TeV flux depends on the
surrounding medium density and on the fraction of thermal energy carried by the
magnetic field, epsilon_B: It ranges from ~10^{-7} erg cm^-2 s^-1 in the case
of typical ISM density and epsilon_B <~ 10^{-4} to 10^{-10} erg cm^-2 s^-1 in
the case of a source surrounded by a wind and epsilon_B ~ 10^{-0.5}; (iii) The
sub-TeV flux is detectable by high energy gamma-ray experiments such as HESS,
MAGIC, MILAGRO, and VERITAS; (iv) Combined ~1 keV, ~1 GeV and sub-TeV
observations will allow to determine both epsilon_B and the ambient medium
density; (v) The spectra depend only weakly on the spectral index of the energy
distribution of the accelerated electrons. Pion production energy loss of high
energy protons may contribute significantly in the wind case to the luminosity
of high energy photons. However, it is difficult to distinguish in this case
between the electron and proton contributions since the spectral shape is
determined primarily by the energy dependence of the pair production optical
depth.
