The relationship between anomalous (re-entrant) melting and the features of the repulsive part of the intermolecular potential is studied in one-component systems with radially symmetric interactions. By making use of the Lennard-Jones-Devonshire cell model, we derive a single-phase criterion for the occurrence of a temperature maximum in the melting line. The criterion is tested against numerical simulation results for a number of isotropic interaction models.