The alpha isoform interacts with DNA-repair protein XRCC1 and can correct defective DNA strand-break repair and sister chromatid exchange following treatment with ionizing radiation and alkylating agents. The beta isoform does not interact with XRCC1 and may be specifically involved in the completion of homologous recombination events that occur during meiotic prophase. ATP + (deoxyribonucleotide)n-3'-hydroxyl + 5'-phospho-(deoxyribonucleotide)m = (deoxyribonucleotide)n+m + AMP + diphosphate. Belongs to the ATP-dependent DNA ligase family.