Let
R
R
be a connected noetherian commutative ring, and let
G
G
be a simply connected reductive group over
R
R
of isotropic rank
≥
2
\ge 2
. The elementary subgroup
E
(
R
)
E(R)
of
G
(
R
)
G(R)
is the subgroup generated by
U
P
+
(
R
)
U_{P^+}(R)
and
U
P
−
(
R
)
U_{P^-}(R)
, where
U
P
±
U_{P^\pm }
are the unipotent radicals of two opposite parabolic subgroups
P
±
P^\pm
of
G
G
. Assume that
2
∈
R
×
2\in R^\times
if
G
G
is of type
B
n
,
C
n
,
F
4
,
G
2
B_n,C_n,F_4,G_2
and
3
∈
R
×
3\in R^\times
if
G
G
is of type
G
2
G_2
. We prove that the congruence kernel of
E
(
R
)
E(R)
, defined as the kernel of the natural homomorphism
E
(
R
)
^
→
E
(
R
)
¯
\widehat {E(R)}\to \overline {E(R)}
between the profinite completion of
E
(
R
)
E(R)
and the congruence completion of
E
(
R
)
E(R)
with respect to congruence subgroups of finite index, is central in
E
(
R
)
^
\widehat {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
)
E(R)
if
R
R
is a local ring.