Catalyzes the ATP-dependent phosphorylation of N-acetyl-L-glutamate. ATP + N-acetyl-L-glutamate = ADP + N-acetyl-L-glutamyl 5-phosphate Amino-acid biosynthesis; L-arginine biosynthesis; N(2)-acetyl-L-ornithine from L-glutamate: step 2/4. Homodimer. Belongs to the acetylglutamate kinase family. ArgB subfamily.