Phosphorylates the deoxyribonucleosides deoxycytidine, deoxyguanosine and deoxyadenosine (PubMed:1996353, PubMed:12808445, PubMed:18377927, PubMed:19159229, PubMed:20614893, PubMed:20637175). Has broad substrate specificity, and does not display selectivity based on the chirality of the substrate. It is also an essential enzyme for the phosphorylation of numerous nucleoside analogs widely employed as antiviral and chemotherapeutic agents (PubMed:12808445). 2'-deoxycytidine + a ribonucleoside 5'-triphosphate = a ribonucleoside 5'-diphosphate + dCMP + H(+) 2'-deoxyadenosine + ATP = ADP + dAMP + H(+) 2'-deoxyguanosine + ATP = ADP + dGMP + H(+) Homodimer. Phosphorylated and activated in vitro upon phosphorylation at Ser-74 by CSNK1D/CK1. Belongs to the DCK/DGK family. Was shown to be phosphorylated and activated by CSNK1D/CK1 in vitro but probably not in vivo.