MOTIVATION: Genetic variation in regulatory elements can alter transcription factor (TF) binding by mutating a TF binding motif, which in turn may affect the activity of the regulatory elements. However, it is unclear which motifs are prone to impact transcriptional regulation if mutated. Current motif analysis tools either prioritize TFs based on motif enrichment without linking to a function or are limited in their applications due to the assumption of linearity between motifs and their functional effects. RESULTS: We present MAGGIE (Motif Alteration Genome-wide to Globally Investigate Elements), a novel method for identifying motifs mediating TF binding and function. By leveraging measurements from diverse genotypes, MAGGIE uses a statistical approach to link mutations of a motif to changes of an epigenomic feature without assuming a linear relationship. We benchmark MAGGIE across various applications using both simulated and biological datasets and demonstrate its improvement in sensitivity and specificity compared with the state-of-the-art motif analysis approaches. We use MAGGIE to gain novel insights into the divergent functions of distinct NF-κB factors in pro-inflammatory macrophages, revealing the association of p65-p50 co-binding with transcriptional activation and the association of p50 binding lacking p65 with transcriptional repression. AVAILABILITY AND IMPLEMENTATION: The Python package for MAGGIE is freely available at https://github.com/zeyang-shen/maggie. The accession number for the NF-κB ChIP-seq data generated for this study is Gene Expression Omnibus: GSE144070. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.