In N = 1 supergravity, the scalar potential may have supersymmetric (SUSY) and non-supersymmetric Minkowski vacua (associated with supersymmetric and physical phases) with vanishing energy density. In the supersymmetric Minkowski (second) phase, some breakdown of SUSY may be induced by nonperturbative effects in the observable sector that give rise to a tiny positive vacuum energy density. Postulating the exact degeneracy of the physical and second vacua as well as assuming that at high energies the couplings in both phases are almost identical, one can estimate the dark energy density in these vacua. It is mostly determined by the SUSY breaking scale M-s in the physical phase. Exploring the two-loop renormalization group (RG) flow of couplings in these vacua, we find that the measured value of the cosmological constant can be reproduced if M-s varies from 20 TeV to 400 TeV. We also argue that this prediction for the SUSY breaking scale is consistent with the upper bound on M-s in the higgsino dark matter scenario.