Phosphorylates the deoxyribonucleosides deoxyadenosine, deoxycytidine and deoxyguanosine with highest activity against deoxyguanosine followed by deadenosine and then deoxycytidine (PubMed:27906638). Shows only very minor activity against deoxyuridine and deoxythymidine (PubMed:27906638). 2'-deoxyguanosine + ATP = ADP + dGMP + H(+) 2'-deoxyadenosine + ATP = ADP + dAMP + H(+) 2'-deoxycytidine + a ribonucleoside 5'-triphosphate = a ribonucleoside 5'-diphosphate + dCMP + H(+) kcat is 1.26 sec(-1) with deoxyguanosine as substrate. kcat is 4.87 sec(-1) with deoxyadenosine as substrate. kcat is 0.42 sec(-1) with deoxycytidine as substrate. kcat is 0.36 sec(-1) with deoxyuridine as substrate. kcat is 0.14 sec(-1) with deoxythymidine as substrate. Homodimer. Belongs to the DCK/DGK family.