Objective. Multi-phase computed tomography (CT) has become a leading modality for identifying hepatic tumors. Nevertheless, the presence of misalignment in the images of different phases poses a challenge in accurately identifying and analyzing the patient’s anatomy. Conventional registration methods typically concentrate on either intensity-based features or landmark-based features in isolation, so imposing limitations on the accuracy of the registration process. Method. We establish a nonrigid cycle-registration network that leverages semi-supervised learning techniques, wherein a point distance term based on Euclidean distance between registered landmark points is introduced into the loss function. Additionally, a cross-distillation strategy is proposed in network training to further improve registration performance which incorporates response-based knowledge concerning the distances between feature points. Results. We conducted experiments using multi-centered liver CT datasets to evaluate the performance of the proposed method. The results demonstrate that our method outperforms baseline methods in terms of target registration error. Additionally, Dice scores of the warped tumor masks were calculated. Our method consistently achieved the highest scores among all the comparing methods. Specifically, it achieved scores of 82.9% and 82.5% in the hepatocellular carcinoma and the intrahepatic cholangiocarcinoma dataset, respectively. Significance. The superior registration performance indicates its potential to serve as an important tool in hepatic tumor identification and analysis.