The accurate identification of high-quality correspondences is a prerequisite task in feature-based point cloud registration. However, it is extremely challenging to handle the fusion of local and global features due to feature redundancy and complex spatial relationships. Given that Gestalt principles provide key advantages in analyzing local and global relationships, we propose a novel Gestalt-guided Parallel Interaction Network via orthogonal geometric consistency (GPI-Net) in this paper. It utilizes Gestalt principles to facilitate complementary communication between local and global information. Specifically, we introduce an orthogonal integration strategy to optimally reduce redundant information and generate a more compact global structure for high-quality correspondences. To capture geometric features in correspondences, we leverage a Gestalt Feature Attention (GFA) block through a hybrid utilization of self-attention and cross-attention mechanisms. Furthermore, to facilitate the integration of local detail information into the global structure, we design an innovative Dual-path Multi-Granularity parallel interaction aggregation (DMG) block to promote information exchange across different granularities. Extensive experiments on various challenging tasks demonstrate the superior performance of our proposed GPI-Net in comparison to existing methods. The code will be released at https://github.com/gwk429/GPI-Net.