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Pixel-level annotation remains a major bottleneck in medical image segmentation, making weak supervision an attractive yet under-constrained alternative. We propose OBBSeg, an intermediate supervision paradigm guided by Oriented Bounding Boxes (OBBs) that bridges the gap between full and weak supervision. By jointly encoding spatial extent and orientation, OBBs provide compact geometric supervision that better aligns with elongated or anisotropic lesions, reducing the ambiguity of coarse box annotations. To mitigate the inherent rectangular bias of OBBs, we introduce a Mask-to-OBB loss, a differentiable formulation that enforces geometric consistency between predicted masks and OBB regions. Furthermore, we incorporate prompt-driven semantic guidance through two complementary modules-PAFE and DBFE-which enhance foreground representation and suppress background interference. Extensive experiments on 13 datasets across 5 imaging modalities show that OBBSeg not only outperforms existing weakly supervised methods but also achieves performance comparable to fully supervised approaches, demonstrating its potential for efficient and scalable medical image segmentation. The code is available at this https URL.