  The flux of cosmic ray antiprotons from neutralino annihilations in the
galactic halo is computed for a large sample of models in the Minimal
Supersymmetric extension of the Standard Model. We also revisit the problem of
estimating the background of low-energy cosmic ray induced secondary
antiprotons, taking into account their subsequent interactions (and energy
loss) and the presence of nuclei in the interstellar matter.
  We point out that in some cases the optimal kinetic energy to search for a
signal from supersymmetric dark matter is above several GeV, rather than the
traditional sub-GeV region. The large astrophysical uncertainties involved do
not allow the exclusion of any of the MSSM models we consider, on the basis of
current data.
