Plays a role in the synthesis of nucleoside triphosphates. This activity may optimize the replication of the AT-rich (73%) viral genome in a thymidine-limited host environment. a 2'-deoxyribonucleoside 5'-diphosphate + ATP = a 2'-deoxyribonucleoside 5'-triphosphate + ADP a ribonucleoside 5'-diphosphate + ATP = a ribonucleoside 5'-triphosphate + ADP KM values are below 10 uM for dCDP, dCTP and dUTP. Belongs to the NDK family.