We discuss an extension of a recent result of A. Rapinchuk and I. Rapinchuk on the centrality of the congruence kernel of the elementary subgroup of a Chevalley (i.e. split) simple algebraic group to the case of isotropic groups. Namely, we prove that for any simply connected simple group scheme G of isotropic rank at least 2 over a Noetherian commutative ring R, the congruence kernel of its elementary subgroup E(R) is central in E(R). Along the way, we define the Steinberg group functor St(-) associated to an isotropic group G as above, and show that for a local ring R, St(R) is a central covering of E(R).