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We propose a Majoron-like extension of the Standard Model with an extra global U(1)X-symmetry where neutrino masses are generated through an inverse seesaw mechanism at the 1-loop level. In contrast to the tree-level inverse seesaw, our framework contains dark matter (DM) candidates stabilized by a residual Z2-symmetry surviving spontaneous breaking of the U(1)X-group. We explore the case in which the DM is a Majorana fermion. Furthermore, we provide parameter space regions allowed by current experimental constraints coming from the dark matter relic abundance, (in)direct detection, and charged lepton flavor violation.