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Deep neural network based speaker recognition systems can easily be deceived by an adversary using minuscule imperceptible perturbations to the input speech samples. These adversarial attacks pose serious security threats to the speaker recognition systems that use speech biometric. To address this concern, in this work, we propose a new defense mechanism based on a hybrid adversarial training (HAT) setup. In contrast to existing works on countermeasures against adversarial attacks in deep speaker recognition that only use class-boundary information by supervised cross-entropy (CE) loss, we propose to exploit additional information from supervised and unsupervised cues to craft diverse and stronger perturbations for adversarial training. Specifically, we employ multi-task objectives using CE, feature-scattering (FS), and margin losses to create adversarial perturbations and include them for adversarial training to enhance the robustness of the model. We conduct speaker recognition experiments on the Librispeech dataset, and compare the performance with state-of-the-art projected gradient descent (PGD)-based adversarial training which employs only CE objective. The proposed HAT improves adversarial accuracy by absolute 3.29% and 3.18% for PGD and Carlini-Wagner (CW) attacks respectively, while retaining high accuracy on benign examples.