DNA ligase that catalyzes the formation of phosphodiester linkages between 5'-phosphoryl and 3'-hydroxyl groups in double-stranded DNA using NAD as a coenzyme and as the energy source for the reaction. It is essential for DNA replication and repair of damaged DNA. NAD(+) + (deoxyribonucleotide)n-3'-hydroxyl + 5'-phospho-(deoxyribonucleotide)m = (deoxyribonucleotide)n+m + AMP + beta-nicotinamide D-nucleotide. Displays maximal in vitro activity at high salt levels. Deletion of both ligA and ligN is lethal. Belongs to the NAD-dependent DNA ligase family. LigA subfamily.