Learning-based medical image registration has achieved performance parity with conventional methods while demonstrating a substantial advantage in computational efficiency. However, learning-based registration approaches lack generalizability across diverse clinical scenarios, requiring the laborious development of multiple isolated networks for specific registration tasks, e.g., inter-/intra-subject registration or organ-specific alignment. % To overcome this limitation, we propose \textbf{UniReg}, the first interactive foundation model for medical image registration, which combines the precision advantages of task-specific learning methods with the generalization of traditional optimization methods. Our key innovation is a unified framework for diverse registration scenarios, achieved through a conditional deformation field estimation within a unified registration model. This is realized through a dynamic learning paradigm that explicitly encodes: (1) anatomical structure priors, (2) registration type constraints (inter/intra-subject), and (3) instance-specific features, enabling the generation of scenario-optimal deformation fields. % Through comprehensive experiments encompassing $90$ anatomical structures at different body regions, our UniReg model demonstrates comparable performance with contemporary state-of-the-art methodologies while achieving ~50\% reduction in required training iterations relative to the conventional learning-based paradigm. This optimization contributes to a significant reduction in computational resources, such as training time. Code and model will be available.