Catalyzes the ATP-dependent phosphorylation of 2-deoxy-D-ribose to 2-deoxy-D-ribose 5-phosphate (dRib-5P), allowing the use of deoxyribose as the sole carbon source. Can also use D-ribose and 2-deoxy-D-ribitol, with lower efficiency. Several ribo- and deoxyribonucleotides can replace ATP as phosphoryl donor