Face recognition has evolved significantly with the advancement of deep learning techniques, enabling its widespread adoption in various applications requiring secure authentication. However, this progress has also increased its exposure to presentation attacks, including face morphing, which poses a serious security threat by allowing one identity to impersonate another. Therefore, modern face recognition systems must be robust against such attacks. In this work, we propose a novel approach for training deep networks for face recognition with enhanced robustness to face morphing attacks. Our method modifies the classification task by introducing a dual-branch classification strategy that effectively handles the ambiguity in the labeling of face morphs. This adaptation allows the model to incorporate morph images into the training process, improving its ability to distinguish them from bona fide samples. Our strategy has been validated on public benchmarks, demonstrating its effectiveness in enhancing robustness against face morphing attacks. Furthermore, our approach is universally applicable and can be integrated into existing face recognition training pipelines to improve classification-based recognition methods.