The integration of multi-omics single-cell data remains challenging due to high-dimensionality and complex inter-modality relationships. To address this, we introduce MoRE-GNN (Multi-omics Relational Edge Graph Neural Network), a heterogeneous graph autoencoder that combines graph convolution and attention mechanisms to dynamically construct relational graphs directly from data. Evaluations on six publicly available datasets demonstrate that MoRE-GNN captures biologically meaningful relationships and outperforms existing methods, particularly in settings with strong inter-modality correlations. Furthermore, the learned representations allow for accurate downstream cross-modal predictions. While performance may vary with dataset complexity, MoRE-GNN offers an adaptive, scalable and interpretable framework for advancing multi-omics integration.