Identifying transcriptional enhancers and their target genes is essential for understanding gene regulation and the impact of human genetic variation on disease. Here we create and evaluate a resource of >13 million enhancer-gene regulatory interactions across 352 cell types and tissues, by integrating predictive models, measurements of chromatin state and 3D contacts, and large-scale genetic perturbations generated by the ENCODE Consortium. We first create a systematic benchmarking pipeline to compare predictive models, assembling a dataset of 10,411 element-gene pairs measured in CRISPR perturbation experiments, >30,000 fine-mapped eQTLs, and 569 fine-mapped GWAS variants linked to a likely causal gene. Using this framework, we develop a new predictive model, ENCODE-rE2G, that achieves state-of-the-art performance across multiple prediction tasks, demonstrating a strategy involving iterative perturbations and supervised machine learning to build increasingly accurate predictive models of enhancer regulation.