This paper proposes a framework for generating adversarial utterances for speaker verification systems. Our main idea is to formulate an optimization problem to generate adversarial utterances that fool speaker verification models and solve it by a second-order optimization method. We first present our algorithm, which uses the first-order Gauss-Newton method, and then extend it to second-order Quasi-Newton methods. Our experiments on the VoxCeleb 1 dataset show that the proposed method can fool a speaker verification system with a smaller degree of perturbations than those of conventional methods. We also show that second-order optimization methods are effective for finding small perturbations.