Medical image segmentation is critical for efficient diagnosis of diseases and treatment planning. In recent years, convolutional neural networks (CNN)-based methods, particularly U-Net and its variants, have achieved remarkable results on medical image segmentation tasks. However, they do not always work consistently on images with complex structures and large variations in regions of interest (ROI). This could be due to the fixed geometric structure of the receptive fields used for feature extraction and repetitive down-sampling operations that lead to information loss. To overcome these problems, the standard U-Net architecture is modified in this work by replacing the convolution block with a dilated convolution block to extract multi-scale context features with varying sizes of receptive fields, and adding a dilated inception block between the encoder and decoder paths to alleviate the problem of information recession and the semantic gap between features. Furthermore, the input of each dilated convolution block is added to the output through a squeeze and excitation unit, which alleviates the vanishing gradient problem and improves overall feature representation by re-weighting the channel-wise feature responses. The original inception block is modified by reducing the size of the spatial filter and introducing dilated convolution to obtain a larger receptive field. The proposed network was validated on three challenging medical image segmentation tasks with varying size ROIs: lung segmentation on chest X-ray (CXR) images, skin lesion segmentation on dermoscopy images and nucleus segmentation on microscopy cell images. Improved performance compared to state-of-the-art techniques demonstrates the effectiveness and generalisability of the proposed Dilated Convolution and Inception blocks-based U-Net (DCI-UNet).