The effect of the Gaussian curvature in the rigid string action on the interquark potential is investigated. The linearized equations of motion and boundary conditions, following from the modified string action, are obtained. The equation, defining the eigenfrequency spectrum of the string oscillations is derived. On this basis, the interquark potential, generated by the string is calculated in one-loop approximation. A substantial influence of the topological term in the string action on the interquark potential at the distances of hadronic size order or less is revealed.