MOTIVATION: Representation learning has revolutionized sequence-based prediction of protein function and subcellular localization. Protein networks are an important source of information complementary to sequences, but the use of protein networks has proven to be challenging in the context of machine learning, especially in a cross-species setting. RESULTS: We leveraged the STRING database of protein networks and orthology relations for 1322 eukaryotes to generate network-based cross-species protein embeddings. We did this by first creating species-specific network embeddings and subsequently aligning them based on orthology relations to facilitate direct cross-species comparisons. We show that these aligned network embeddings ensure consistency across species without sacrificing quality compared to species-specific network embeddings. We also show that the aligned network embeddings are complementary to sequence embedding techniques, despite the use of sequence-based orthology relations in the alignment process. Finally, we validated the embeddings by using them for two well-established tasks: subcellular localization prediction and protein function prediction. Training logistic regression classifiers on aligned network embeddings and sequence embeddings improved the accuracy over using sequence alone, reaching performance numbers close to state-of-the-art deep-learning methods. AVAILABILITY AND IMPLEMENTATION: The source code and scripts for generating the network-based cross-species protein embeddings are available at https://github.com/deweihu96/SPACE. Precomputed network embeddings and sequence embeddings for all eukaryotic proteins are included in STRING version 12.0 (https://string-db.org/cgi/download).