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Automatic segmentation of abdominal organs in computed tomography (CT) images can support radiation therapy and image-guided surgery workflows. Developing of such automatic solutions remains challenging mainly owing to complex organ interactions and blurry boundaries in CT images. To address these issues, we focus on effective spatial context modeling and explicit edge segmentation priors. Accordingly, we propose a 3D network with four main components trained end-to-end including shared encoder, edge detector, decoder with edge skip-connections (ESCs) and recurrent feature propagation head (RFP-Head). To capture wide-range spatial dependencies, the RFP-Head propagates and harvests local features through directed acyclic graphs (DAGs) formulated with recurrent connections in an efficient slice-wise manner, with regard to spatial arrangement of image units. To leverage edge information, the edge detector learns edge prior knowledge specifically tuned for semantic segmentation by exploiting intermediate features from the encoder with the edge supervision. The ESCs then aggregate the edge knowledge with multi-level decoder features to learn a hierarchy of discriminative features explicitly modeling complementarity between organs' interiors and edges for segmentation. We conduct extensive experiments on two challenging abdominal CT datasets with eight annotated organs. Experimental results show that the proposed network outperforms several state-of-the-art models, especially for the segmentation of small and complicated structures (gallbladder, esophagus, stomach, pancreas and duodenum). The code will be publicly available.