We propose a novel multi-level dilated residual neural network, an extension of the classical U-Net architecture, for biomedical image segmentation. U-Net is the most popular deep neural architecture for biomedical image segmentation, however, despite being state-of-the-art, the model has a few limitations. In this study, we suggest replacing convolutional blocks of the classical U-Net with multi-level dilated residual blocks, resulting in enhanced learning capability. We also propose to incorporate a non-linear multi-level residual blocks into skip connections to reduce the semantic gap and to restore the information lost when concatenating features from encoder to decoder units. We evaluate the proposed approach on five publicly available biomedical datasets with different imaging modalities, including electron microscopy, magnetic resonance imaging, histopathology, and dermoscopy, each with its own segmentation challenges. The proposed approach consistently outperforms the classical U-Net by 2%, 3%, 6%, 8%, and 14% relative improvements in dice coefficient, respectively for magnetic resonance imaging, dermoscopy, histopathology, cell nuclei microscopy, and electron microscopy modalities. The visual assessments of the segmentation results further show that the proposed approach is robust against outliers and preserves better continuity in boundaries compared to the classical U-Net and its variant, MultiResUNet.