Catalyzes the methylation of both C-2 and C-7 of uroporphyrinogen III leading to precorrin-1 and precorrin-2; their oxidative esterification gives respectively factor I octamethyl ester and sirohydrochlorin (By similarity). Inactivation of uroporphyrinogen-III methyltransferase results in the loss of nitrite and nitric oxide reductase activities, but not of nitrous oxide reductase activity. Likely involved in heme D1 biosynthesis. 2 S-adenosyl-L-methionine + uroporphyrinogen III = H(+) + precorrin-2 + 2 S-adenosyl-L-homocysteine Porphyrin-containing compound metabolism; siroheme biosynthesis; precorrin-2 from uroporphyrinogen III: step 1/1. Belongs to the precorrin methyltransferase family.