Entity and Relation Extraction (ERE) is typically handled in a pipeline manner. However, such an approach relies only on the output of the preceding task, resulting in limited information interaction between named entity recognition and relation extraction, and is susceptible to error propagation. To address these challenges, a Memory-Enhanced model for Entity and Relation Extraction (MEERE) was proposed. This model introduced a memory-like mechanism, allowing each task not only to utilize the output of the preceding task, but also to influence it in reverse, thereby capturing complex interactions between entities and relations. To further mitigate error propagation, an entity span screening mechanism was incorporated. This mechanism dynamically screened and verified entity spans in the joint module, ensuring that only high-quality entities were used for relation extraction, thus enhancing the robustness and accuracy of the model. A table decoding method was finally employed to handle relation overlap. Experimental results on three widely used benchmark datasets (ACE05, SciERC, and CoNLL04) demonstrated significant advantages of MEERE in ERE tasks. In specific, on the CoNLL04 dataset, MEERE outperformed Tab-Seq model in both named entity recognition and relation extraction tasks with a 0.5 percentage point increase in named entity recognition F1-score and a 3.0 percentage point improvement in relation strict evaluation F1-score; compared to PURE-F model, MEERE achieved no less than a ninefold acceleration effect with improved relation extraction performance. These findings confirm the effectiveness of the proposed memory enhancement model in exploring interactions between entities and relations.