Catalyzes the ATP-dependent phosphorylation of both cell wall (peptidoglycan) amino sugars, N-acetylmuramic acid (MurNAc) and N-acetylglucosamine (GlcNAc), at the 6-hydroxyl group. Neither the non-N-acetylated forms of the cell wall sugars, i.e., glucosamine and/or muramic acid, nor epimeric hexoses or 1,6-anhydro-MurNAc are substrates for the enzyme. May have a role in the rescue of the murein sugars GlcNAc and MurNAc released from muropeptides during cell wall turnover in C.acetobutylicum. ATP + N-acetyl-D-glucosamine = ADP + H(+) + N-acetyl-D-glucosamine 6-phosphate ATP + N-acetyl-D-muramate = ADP + H(+) + N-acetyl-D-muramate 6-phosphate kcat is 65.0 sec(-1) with GlcNAc as substrate. kcat is 42.8 sec(-1) with MurNAc as substrate. Optimum pH is 7.5 to 9.0. Retains half maximal activity at about pH 6.5 and 10.5 and is inactive at pH 5 and below. Cell wall biogenesis; peptidoglycan recycling. Belongs to the eukaryotic-type N-acetylglucosamine kinase family.