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Emotion recognition using electroencephalogram (EEG) encompasses two main scenarios: classifying discrete labels and regressing continuously tagged labels. While numerous algorithms have been proposed for classification tasks, there are only a few methods available for regression tasks. In the case of emotion regression, the labels are continuous in time, making it essential to learn temporal dynamic patterns. Previous studies have utilized long short-term memory (LSTM) and temporal convolutional neural networks (TCN) to capture temporal contextual information from EEG feature vectors. However, these approaches do not effectively extract the spatial patterns of EEG. To address this limitation and enhance regression and classification performances, we introduce a novel unified model called MASA-TCN for EEG emotion regression and classification tasks. The MASA-TCN model incorporates a space-aware temporal layer, enabling TCN to learn from spatial relations among EEG electrodes. Additionally, a novel multi-anchor block with attentive fusion is proposed to learn dynamic temporal dependencies. Experimental results on two publicly available datasets demonstrate that MASA-TCN outperforms state-of-the-art methods for both EEG emotion regression and classification tasks. The code for MASA-TCN is available at https://github.com/yi-ding-cs/MASA-TCN.