Catalyzes the phosphorylation of the position 2 hydroxy group of 4-diphosphocytidyl-2C-methyl-D-erythritol. 4-CDP-2-C-methyl-D-erythritol + ATP = 4-CDP-2-C-methyl-D-erythritol 2-phosphate + ADP + H(+) Divalent metal ions. Preferably magnesium. Isoprenoid biosynthesis; isopentenyl diphosphate biosynthesis via DXP pathway; isopentenyl diphosphate from 1-deoxy-D-xylulose 5-phosphate: step 3/6. Belongs to the GHMP kinase family. IspE subfamily.