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Visualizing subtle vascular motions in endoscopic surgery is crucial for surgical precision and decision-making, yet remains challenging due to the complex and dynamic nature of surgical scenes. To address this, we introduce EndoControlMag, a training-free, Lagrangian-based framework with mask-conditioned vascular motion magnification tailored to endoscopic environments. Our approach features two key modules: a Periodic Reference Resetting (PRR) scheme that divides videos into short overlapping clips with dynamically updated reference frames to prevent error accumulation while maintaining temporal coherence, and a Hierarchical Tissue-aware Magnification (HTM) framework with dual-mode mask dilation. HTM first tracks vessel cores using a pretrained visual tracking model to maintain accurate localization despite occlusions and view changes. It then applies one of two adaptive softening strategies to surrounding tissues: motion-based softening that modulates magnification strength proportional to observed tissue displacement, or distance-based exponential decay that simulates biomechanical force attenuation. This dual-mode approach accommodates diverse surgical scenarios-motion-based softening excels with complex tissue deformations while distance-based softening provides stability during unreliable optical flow conditions. We evaluate EndoControlMag on our EndoVMM24 dataset spanning four different surgery types and various challenging scenarios, including occlusions, instrument disturbance, view changes, and vessel deformations. Quantitative metrics, visual assessments, and expert surgeon evaluations demonstrate that EndoControlMag significantly outperforms existing methods in both magnification accuracy and visual quality while maintaining robustness across challenging surgical conditions. The code, dataset, and video results are available at https://szupc.github.io/EndoControlMag/.