  Possibility of a Right-Handed (RH) neutrino being a Goldstone fermion of a
spontaneously broken global $U(1)$ symmetry in a supersymmetric theory is
considered. This fermion obtains mass from the supergravity effects leading to
a RH neutrino at the electroweak scale with a mass similar to the gravitino
mass. A prototype model realizing this scenario contains just three gauge
singlet superfields needed for the type I seesaw mechanism. Masses of the other
two neutrinos are determined by the $U(1)$ breaking scale which too can be
around the electroweak scale. Light neutrinos obtain their masses in this
scenario through (a) mixing with the RH neutrinos (type I seesaw), (b) mixing
with neutralinos ($R$-parity breaking), (c) indirectly through mixing of the RH
neutrinos with neutralinos, and (d) radiative corrections. All these
contributions are described by the same set of a small number of underlying
parameters and provide a very constrained and predictive framework for the
neutrino masses which is investigated in detail for various choices of $U(1)$
symmetries. It is found that flavour independent $U(1)$ symmetries cannot
describe neutrino masses if the soft supersymmetry breaking terms are flavour
universal and one needs to consider flavour dependent symmetries. Considering a
particular example of $L_\mu - L_\tau$ symmetry, it is shown that viable
neutrino masses and mixing can be obtained without introducing any flavour
violation in the soft sector. The leptonic couplings of Majoron are worked out
in the model and shown to be consistent with various laboratory, astrophysical
and cosmological constraints. The neutrino data allows sizeable couplings
between the RH neutrinos and Higgsinos which can be used to probe the
pseudo-Goldstone fermion at colliders through its displaced decay vertex.
