Phosphorylates uridine and cytidine to uridine monophosphate and cytidine monophosphate (PubMed:11306702). Does not phosphorylate deoxyribonucleosides or purine ribonucleosides (PubMed:11306702). Can use ATP or GTP as a phosphate donor (PubMed:11306702). Can also phosphorylate cytidine and uridine nucleoside analogs such as 6-azauridine, 5-fluorouridine, 4-thiouridine, 5-bromouridine, N(4)-acetylcytidine, N(4)-benzoylcytidine, 5-fluorocytidine, 2-thiocytidine, 5-methylcytidine, and N(4)-anisoylcytidine (PubMed:11306702).