Accurate vessel segmentation is essential for medical image analysis, yet remains challenging due to complex vascular patterns and imaging ambiguity. Most deep models rely on single-pass prediction, limiting their ability to refine uncertain or disconnected regions during inference. To address this limitation, we propose Uncertainty-Guided Conservative Propagation (UGCP), a general plug-in module for vessel segmentation. Instead of directly using a one-shot output as the final prediction, UGCP performs a small number of logit-space update steps to refine the segmentation through local predictions interaction. Predictive uncertainty guides reliable regions to support ambiguous regions, while structure-aware modulation and source-based stabilization reduce unreliable propagation and excessive drift. The module is differentiable and can be trained end-to-end with different segmentation networks. We evaluate UGCP on four public vessel segmentation datasets covering 2D and 3D tasks, including retinal vessel, coronary artery, and cerebral vessel segmentation. Experiments with convolutional neural network-based and Transformer-based backbones show consistent improvements in Dice similarity coefficient, centerline Dice, and 95th percentile Hausdorff distance. Further analysis demonstrates that UGCP reduces vessel disconnections and improves structural consistency with limited additional computation. The code will be made available at https://github.com/chenzhao2023/UGC_PR.