Catalyzes the ATP-dependent phosphorylation of 3-oxo-tetronate to 3-oxo-tetronate 4-phosphate. 3-dehydro-L-erythronate + ATP = 3-dehydro-4-O-phospho-L-erythronate + ADP + H(+) 3-dehydro-D-erythronate + ATP = 3-dehydro-4-O-phospho-D-erythronate + ADP + H(+) Belongs to the four-carbon acid sugar kinase family.