Speech enhancement approaches based on neural networks, aim to learn a noisy-to-clean transformation using a supervised learning paradigm. However, networks trained in this way may not be effective at handling languages and types of noise that were not present in the training data. To address this issue, this study focuses on unsupervised domain adaptation, specifically for large-domain-gap cases. In this setup, we have noisy speech data from the new domain but the corresponding clean speech data are not available. We propose an adaptation method that is based on domain-adversarial training followed by iterative self-training where the quality of the estimated speech used as pseudo labels is monitored by the performance of the adapted network on labeled data from the source domain. Experimental results show that our method effectively mitigates the domain mismatch between training and test sets, and surpasses the current baseline.