We analyze the near‐threshold behavior of a circularly symmetric distributed feedback laser by developing a coupled‐mode theory analysis for all azimuthal modes. We show that the equations that describe the low‐order azimuthal modes are, to a very good approximation, the same as those for the one‐dimensional (linear) distributed feedback laser. We examine the behavior of higher‐order azimuthal modes by numerically solving the exact coupled‐mode equations. We find that while a significant amount of mode discrimination exists among radial (longitudinal) modes, as in the one‐dimensional distributed feedback laser, there is a much smaller degree of discrimination among azimuthal modes, indicating probability of multimode operation. Despite the multimode behavior, we find that the frequency bandwidth associated with modes that do lase ought to be smaller than the spacing between Fabry‐Perot modes of a typical semiconductor laser. This laser is an excellent candidate for a surface‐emitting laser—it should have a superb quality output beam and is well‐suited for array operation.