Existing weakly-supervised camouflaged object detection (WSCOD) methods have much difficulty in detecting accurate object boundaries due to insufficient and imprecise boundary supervision in scribble annotations. Drawing inspiration from human perception that discerns camouflaged objects by incorporating both object region and boundary information, we propose a novel Mutual Interaction Network (MiNet) for scribble-based WSCOD to alleviate the detection difficulty caused by insufficient scribbles. The proposed MiNet facilitates mutual reinforcement between region and edge cues, thereby integrating more robust priors to enhance detection accuracy. In this paper, we first construct an edge cue refinement net, featuring a core region-aware guidance module (RGM) aimed at leveraging the extracted region feature as a prior to generate the discriminative edge map. By considering both object semantic and positional relationships between edge feature and region feature, RGM highlights the areas associated with the object in the edge feature. Subsequently, to tackle the inherent similarity between camouflaged objects and the surroundings, we devise a region-boundary refinement net. This net incorporates a core edge-aware guidance module (EGM), which uses the enhanced edge map from the edge cue refinement net as guidance to refine the object boundaries in an iterative and multi-level manner. Experiments on CAMO, CHAMELEON, COD10K, and NC4K datasets demonstrate that the proposed MiNet outperforms the state-of-the-art methods.