Infinite impulse response (IIR) digital filters with prescribed magnitude and phase responses have been used in many applications. To approximate the prescribed magnitude and phase responses, we propose a new approach to the design of general IIR filters by minimizing the maximum phase error subject to a prescribed or simultaneously minimized maximum magnitude error, where the phase error and magnitude error are controlled by two elliptic constraints respectively with major and minor axes along the desired frequency response. The sequential constrained least-squares method and Levy-Sanathanan-Koerner strategy are used to convert the nonconvex constraints into convex ones, resulting in a series of convex optimization subproblems. Design examples and comparisons with recent methods demonstrate the flexibility and effectiveness of the proposed methods.