The flux of cosmic-ray antiprotons from neutralino annihilations in the Gal
actic halo is computed for a large sample of models in the minimal supersym
metric extension of the standard model (MSSM). We also revisit the problem
of estimating the background of low-energy cosmic-ray-induced secondary ant
iprotons, taking into account their subsequent interactions (and energy los
s) and the presence of nuclei in the interstellar matter. We consider a two
-zone diffusion model, with and without a Galactic wind. We find that, give
n the uncertainties in the background predictions, there is no need for a p
rimary (exotic) component to explain current data. However, allowing for a
signal by playing with the uncertainties in the background estimate, we dis
cuss the characteristic features of the supersymmetric models that give a s
atisfactory description of the data. We point out that in some cases, the o
ptimal kinetic energy to search for a signal from supersymmetric dark matte
r is above several GeV, rather than the traditional sub-GeV region. The lar
ge astrophysical uncertainties involved do not, on the other hand, allow th
e exclusion of any of the MSSM models we consider on the basis of data. In
addition to numerical results, we also present convenient parameterizations
of the antiproton yields of all "basic" two-body final states. We also giv
e examples of the yield and differential energy spectrum for a set of super
symmetric models with high rates. We also remark that it is difficult to se
t a limit on the antiproton lifetime from present measurements, since the i
njection of antiprotons from neutralino annihilation can compensate for the
loss from decay.