Catalyzes the reversible reduction of methenyl-H(4)MPT(+) to methylene-H(4)MPT. 5,10-methenyl-5,6,7,8-tetrahydromethanopterin + H2 = 5,10-methylenetetrahydromethanopterin + H(+) Activity requires salt; 100 mM potassium phosphate, potassium chloride, and sodium chloride are equally effective. Thermolabile at 90 degrees Celsius. One-carbon metabolism; methanogenesis from CO(2); 5,10-methylene-5,6,7,8-tetrahydromethanopterin from 5,10-methenyl-5,6,7,8-tetrahydromethanopterin (hydrogen route): step 1/1. Homotetramer. Belongs to the HMD family.