We propose a new seesaw mechanism for neutrino masses within a class of supersymmetric SO(10) models with broken D parity. It is shown that in such scenarios the B-L scale can be as low as TeV without generating inconsistencies with gauge coupling unification nor with the required magnitude of the light neutrino masses. This leads to a possibly light new neutral gauge boson as well as relatively light quasi-Dirac heavy leptons. These particles could be at the TeV scale and mediate lepton flavor and CP violating processes at appreciable levels.
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