Let R be a connected noetherian commutative ring, and let G be a simply connected reductive group over R of isotropic rank ≥ 2. The elementary subgroup E(R) of G(R) is the subgroup generated by U_P+(R) and U_P−(R), where U_P± are the unipotent radicals of two opposite parabolic subgroups P^± of G. Assume that 2 ∈ R^× if G is of type B_n, C_n, F₄, G₂ and 3 ∈ R^× if G is of type G₂. We prove that the congruence kernel of E(R), defined as the kernel of the natural homomorphism E(R) → E(R) between the profinite completion of E(R) and the congruence completion of E(R) with respect to congruence subgroups of finite index, is central in E(R). In the course of the proof, we construct Steinberg groups associated to isotropic reducive groups and show that they are central extensions of E(R) if R is a local ring.