We generalize the linear stability analysis of the axisymmetric self-similar solution of gravity currents from finite-volume releases to include perturbations that depend on both radial and azimuthal coordinates. We show that the similarity solution is stable to sufficiently small perturbations by proving that all perturbation eigenfunctions decay in time. Moreover, asymmetric perturbations are shown to decay more rapidly than axisymmetric perturbations in general. An asymptotic formula for the eigenvalues is derived, which indicates that asymptotic rates of decay of perturbations are given by