  We discuss a scenario in which the supergravity induced soft terms,
conventionally used for breaking supersymmetry, also lead to non-zero Majorana
neutrino masses. The soft terms lead to the spontaneous violation of the lepton
number at the gravitino mass scale $m_{3/2}$ which in turn leads to (i) the
Majorana masses of ${\cal O} (m_{3/2})$ for the right-handed neutrinos and (ii)
the $R$-parity breaking at the same scale. The former contributes to light
neutrino masses through the type I seesaw mechanism, while the latter adds to
it through neutrino-neutralino mixing. Both contributions can scale inversely
with respect to $m_{3/2}$ given that gaugino and Higgsino masses are also of
order $m_{3/2}$. Together, these two contributions adequately explain observed
neutrino masses and mixing. One realization of the scenario also naturally
leads to a $\mu$ parameter of ${\cal O} (m_{3/2})$. Despite the lepton number
symmetry breaking close to the weak scale, the Majoron in the model exhibits
very weak coupling to leptons, satisfying existing constraints on
Majoron-lepton interactions. The right-handed neutrinos in the model have a
large coupling to Higgsinos. This coupling and the relatively large heavy-light
neutrino mixing induced through the seesaw mechanism may lead to the observable
signals at colliders in terms of displaced vertices.
