diff --git a/python/tvm/relay/frontend/onnx.py b/python/tvm/relay/frontend/onnx.py
index 474b688e2ad8..ab0eeb091043 100644
--- a/python/tvm/relay/frontend/onnx.py
+++ b/python/tvm/relay/frontend/onnx.py
@@ -3913,10 +3913,17 @@ class QLinearMatMul(OnnxOpConverter):
     - Only supports 2D input tensors.
     - Not guaranteed to meet the integer-overflow behavior stipulated in the
       ONNX documentation for this operator.
+
+    The QLinearMatMul converter is re-used for MatMulInteger and is adapted for
+    the latter with the optional `expected_out_dtypes` argument.
     """
 
     @classmethod
-    def _impl_v10(cls, inputs, attr, params):
+    def _impl_v10(cls, inputs, attr, params, expected_out_dtypes=None):
+        if expected_out_dtypes is None:
+            # The default QLinearMatMul converter is expected to have one of
+            # these output dtypes.
+            expected_out_dtypes = ["int8", "uint8"]
 
         # Some of the ops used below take scalar-like inputs, and may require either
         # of the following:
@@ -3966,7 +3973,7 @@ def try_resolve_to_const(x, dtype_override=None):
         assert b_zp_type.dtype == b_type.dtype
 
         assert y_scale_type.dtype == "float32"
-        assert y_zp_type.dtype in ["int8", "uint8"]
+        assert y_zp_type.dtype in expected_out_dtypes
 
         # TODO: relax this limitation in a future version of this importer.
         a_rank = len(a_shape)
@@ -4028,6 +4035,11 @@ def try_resolve_to_const(x, dtype_override=None):
         matmul_result_scale_scalar = fold_constant(_op.multiply(a_scale_scalar, b_scale_scalar))
         matmul_result_zp_scalar = _op.const(0, dtype="int32")
 
+        if "int32" in expected_out_dtypes:
+            # This is the adaptation of the QLinearMatMul converter for MatMulInteger,
+            # in the MatMulInteger case we skip the unnecessary requantization step.
+            return matmul_result
+
         # requantize requires y_scale to be constant,
         # if y_scale is not constant, doing dequantize -> quantize
         if isinstance(y_scale_scalar, _expr.Constant):
@@ -4053,6 +4065,58 @@ def try_resolve_to_const(x, dtype_override=None):
         return y
 
 
+class MatMulInteger(OnnxOpConverter):
+    """Operator converter for MatMulInteger."""
+
+    @classmethod
+    def _impl_v10(cls, inputs, attr, params):
+        a = inputs[0]
+        b = inputs[1]
+
+        a_dtype = infer_type(a).checked_type.dtype
+        b_dtype = infer_type(b).checked_type.dtype
+
+        assert a_dtype in ("int8", "uint8"), "MatMulInteger: invalid dtype for first input"
+        assert b_dtype in ("int8", "uint8"), "MatMulInteger: invalid dtype for second input"
+
+        assert a_dtype == b_dtype, "MatMulInteger: input dtypes must match"
+
+        a_scale = _op.const(1.0, dtype="float32")
+        b_scale = _op.const(1.0, dtype="float32")
+        out_scale = _op.const(1.0, dtype="float32")
+
+        a_zero_point = _op.const(0.0, dtype=a_dtype)
+        b_zero_point = _op.const(0.0, dtype=b_dtype)
+        out_zero_point = _op.const(0.0, dtype="int32")
+
+        if len(inputs) == 4:
+            a_zero_point = inputs[2]
+            b_zero_point = inputs[3]
+
+            a_zp_dtype = infer_type(a_zero_point).checked_type.dtype
+            b_zp_dtype = infer_type(b_zero_point).checked_type.dtype
+            assert (
+                a_zp_dtype == a_dtype and b_zp_dtype == b_dtype
+            ), "MatMulInteger: input dtype doesn't match zero point dtype"
+        elif len(inputs) != 2:
+            raise AssertionError(
+                "MatMulInteger op takes 2 or 4 inputs, {} given".format(len(inputs))
+            )
+
+        inputs = [
+            a,
+            a_scale,
+            a_zero_point,
+            b,
+            b_scale,
+            b_zero_point,
+            out_scale,
+            out_zero_point,
+        ]
+
+        return QLinearMatMul.get_converter(10)(inputs, attr, params, expected_out_dtypes=["int32"])
+
+
 class QLinearMul(OnnxOpConverter):
     """Operator converter for QLinearMul from Microsoft onnxruntime contrib opset."""
 
@@ -4781,6 +4845,7 @@ def _get_convert_map(opset):
         "Softsign": Softsign.get_converter(opset),
         "Gemm": Gemm.get_converter(opset),
         "MatMul": MatMul.get_converter(opset),
+        "MatMulInteger": MatMulInteger.get_converter(opset),
         "MatMulInteger16": MatMulInteger16.get_converter(opset),
         "Mod": Mod.get_converter(opset),
         "Xor": Renamer("logical_xor"),
diff --git a/python/tvm/topi/cuda/tensorcore_alter_op.py b/python/tvm/topi/cuda/tensorcore_alter_op.py
index 080ddf28b7c2..0ba428014548 100644
--- a/python/tvm/topi/cuda/tensorcore_alter_op.py
+++ b/python/tvm/topi/cuda/tensorcore_alter_op.py
@@ -167,8 +167,22 @@ def _dense_legalize(attrs, inputs, arg_types):
         return None
 
     (dm, dk, dn), extra_flops_ratio = pad_to_tensorcore(M, K, N, candidates)
+    skip_pad = extra_flops_ratio > 2
+
+    if skip_pad and dtype in ["int8", "uint8"]:
+        skip_pad = False
+        # If tensorcore schedule padding fails, pad to nearest upward 4x4x4 as long as
+        # the additional flops ratio isn't double or more.
+        # Note that 4x4x4 is invalid for tensorcore scheduling, but padding upwards to 4x4x4
+        # doesn't hurt if tensorcore padding has already failed.
+        if M % 4 == 0 and K % 4 == 0 and N % 4 == 0:
+            # No need to pad
+            return None
+        (dm, dk, dn) = _pad_to(M, K, N, (4, 4, 4))
+        extra_flops_ratio = _extra_flops(M, K, N, dm, dk, dn) / (M * K * N)
+        skip_pad = extra_flops_ratio > 2
 
-    if extra_flops_ratio > 2:
+    if skip_pad:
         logger.info("dense pad_to_tensorcore skipped, extra_flops_ratio %s", extra_flops_ratio)
         return None
 
@@ -198,7 +212,7 @@ def pad_to_tensorcore(M, K, N, candidates):
     best_pad = (0, 0, 0)
     for padding in candidates:
         dm, dk, dn = _pad_to(M, K, N, padding)
-        e = (M + dm) * (N + dn) * (K + dk) - M * N * K
+        e = _extra_flops(M, K, N, dm, dk, dn)
         # print(dm, dk, dn, e, flops)
         if e < extra_flops:
             extra_flops = e
@@ -206,6 +220,10 @@ def pad_to_tensorcore(M, K, N, candidates):
     return best_pad, extra_flops / flops
 
 
+def _extra_flops(M, K, N, dm, dk, dn):
+    return (M + dm) * (N + dn) * (K + dk) - M * N * K
+
+
 def _pad_to(M, K, N, PADDING):
     dm, dk, dn = 0, 0, 0
 
diff --git a/tests/python/frontend/onnx/test_forward.py b/tests/python/frontend/onnx/test_forward.py
index 0751f4a2e293..94fd0a5de40b 100644
--- a/tests/python/frontend/onnx/test_forward.py
+++ b/tests/python/frontend/onnx/test_forward.py
@@ -5053,7 +5053,6 @@ def verify_eyelike(indata):
     "test_loop11",
     "test_loop13_seq",
     "test_lstm_batchwise",
-    "test_matmulinteger",
     "test_maxpool_with_argmax_2d_precomputed_pads",
     "test_maxpool_with_argmax_2d_precomputed_strides",
     "test_maxunpool_export_with_output_shape",
diff --git a/tests/python/relay/test_pass_legalize_tensorcore.py b/tests/python/relay/test_pass_legalize_tensorcore.py
index 97860630dea5..0e3c171d87da 100644
--- a/tests/python/relay/test_pass_legalize_tensorcore.py
+++ b/tests/python/relay/test_pass_legalize_tensorcore.py
@@ -249,6 +249,7 @@ def expected():
             a = before()
             a = run_opt_pass(a, transform.Legalize())
             b = run_opt_pass(expected(), transform.InferType())
+
         assert tvm.ir.structural_equal(a, b), "Actual = \n" + str(a) + "Expected = \n" + str(b)
 
     # dense
@@ -259,7 +260,7 @@ def expected():
         _test_legalize_dense((8, 16), (31, 16), (0, 0, 1), dtype)
         _test_legalize_dense((7, 15), (31, 15), (1, 1, 1), dtype)
         _test_legalize_dense((3, 16), (32, 16), (5, 0, 0), dtype)
-        _test_legalize_dense((2, 16), (32, 16), (0, 0, 0), dtype, False)
+        _test_legalize_dense((1, 16), (32, 16), (0, 0, 0), dtype, False)
 
     # Test if units parameter is correctly updated
     _test_legalize_dense((8, 16), (30, 16), (0, 0, 2), "float16", units=30)