Medical image segmentation can provide detailed information for clinical analysis which can be useful for scenarios where the detailed location of a finding is important. Knowing the location of a disease can play a vital role in treatment and decision-making. Convolutional neural network (CNN) based encoder-decoder techniques have advanced the performance of automated medical image segmentation systems. Several such CNN-based methodologies utilize techniques such as spatial- and channel-wise attention to enhance performance. Another technique that has drawn attention in recent years is residual dense blocks (RDBs). The successive convolutional layers in densely connected blocks are capable of extracting diverse features with varied receptive fields and thus, enhancing performance. However, consecutive stacked convolutional operators may not necessarily generate features that facilitate the identification of the target structures. In this paper, we propose a progressive alternating attention network (PAANet). We develop progressive alternating attention dense (PAAD) blocks, which construct a guiding attention map (GAM) after every convolutional layer in the dense blocks using features from all scales. The GAM allows the following layers in the dense blocks to focus on the spatial locations relevant to the target region. Every alternatePAAD block inverts the GAM to generate a reverse attention map which guides ensuing layers to extract boundary and edge-related information, refining the segmentation process. Our experiments on three different biomedical image segmentation datasets exhibit that our PAANet achieves favorable performance when compared to other state-of-the-art methods.