DNA ligase that seals nicks in double-stranded DNA during DNA replication, DNA recombination and DNA repair. Interaction with PCNA enhances ligase activity. DNA polymerase I, DNA ligase and the flap endonuclease may be constitutively associated with the PCNA heterotrimer forming a scanning complex able to couple DNA synthesis and Okazaki fragment maturation. ATP + (deoxyribonucleotide)n-3'-hydroxyl + 5'-phospho-(deoxyribonucleotide)m = (deoxyribonucleotide)n+m + AMP + diphosphate. Ligase activity stimulated by PCNA heterotrimer. Interacts with the PCNA heterotrimer, probably via subunit PCNA3. Belongs to the ATP-dependent DNA ligase family.