Allows the synthesis of deoxyribonucleoside triphosphates necessary for the rapid viral DNA replication (PubMed:14711503). Phosphorylates all four dNMPs (PubMed:5846986). a 2'-deoxyribonucleoside 5'-phosphate + ATP = a 2'-deoxyribonucleoside 5'-diphosphate + ADP Monomer. Expressed in the early phase of the viral replicative cycle.