Catalysis of the reaction: NAD+ + deoxyribonucleotide(n) + deoxyribonucleotide(m) = AMP + nicotinamide nucleotide + deoxyribonucleotide(n+m).
poly(deoxyribonucleotide):poly(deoxyribonucleotide) ligase (AMP-forming, NMN-forming)