GO:0001056:   RNA polymerase III activity
Catalysis of the reaction: nucleoside triphosphate + RNA(n) = diphosphate + RNA(n+1). Utilizes a DNA template that contains an RNA polymerase III specific promoter to direct initiation and catalyses DNA-template-directed extension of the 3"-end of an RNA strand by one nucleotide at a time. Can initiate a chain "de novo".