Point cloud registration is a basic task in computer vision and computer graphics. Recently, deep learning-based end-to-end methods have made great progress in this field. One of the challenges of these methods is to deal with partial-to-partial registration tasks. In this work, we propose a novel end-to-end framework called MCLNet that makes full use of multi-level consistency for point cloud registration. First, the point-level consistency is exploited to prune points located outside overlapping regions. Second, we propose a multi-scale attention module to perform consistency learning at the correspondence-level for obtaining reliable correspondences. To further improve the accuracy of our method, we propose a novel scheme to estimate the transformation based on geometric consistency between correspondences. Compared to baseline methods, experimental results show that our method performs well on smaller-scale data, especially with exact matches. The reference time and memory footprint of our method are relatively balanced, which is more beneficial for practical applications.