Within Open Relation Extraction (ORE) tasks, the Zero-shot ORE method is to generalize undefined relations from predefined relations, while the Unsupervised ORE method is to extract undefined relations without the need for annotations. However, despite the possibility of overlap between predefined and undefined relations in the training data, a unified framework for both Zero-shot and Unsupervised ORE has yet to be established. To address this gap, we propose U-CORE: A Unified Deep Cluster-wise Contrastive Framework for both Zero-shot and Unsupervised ORE, by leveraging techniques from Contrastive Learning (CL) and Clustering.1 U-CORE overcomes the limitations of CL-based Zero-shot ORE methods by employing Cluster-wise CL that preserves both local smoothness as well as global semantics. Additionally, we employ a deep-cluster-based updater that optimizes the cluster center, thus enhancing the accuracy and efficiency of the model. To increase the stability of the model, we adopt Adaptive Self-paced Learning that effectively addresses the data-shifting problems. Experimental results on three well-known datasets demonstrate that U-CORE significantly improves upon existing methods by showing an average improvement of 7.35% ARI on Zero-shot ORE tasks and 15.24% ARI on Unsupervised ORE tasks.