Efficiently joins single-strand breaks in a double-stranded polydeoxynucleotide in an ATP-dependent reaction. Involved in DNA nonhomologous end joining (NHEJ) required for double-strand break repair. ATP + (deoxyribonucleotide)n-3'-hydroxyl + 5'-phospho-(deoxyribonucleotide)m = (deoxyribonucleotide)n+m + AMP + diphosphate. Belongs to the ATP-dependent DNA ligase family.