diff --git a/python/cudf/cudf/core/index.py b/python/cudf/cudf/core/index.py
index 66ab742d4a7..a0d2a161674 100644
--- a/python/cudf/cudf/core/index.py
+++ b/python/cudf/cudf/core/index.py
@@ -1783,15 +1783,12 @@ def __init__(
         elif dtype not in valid_dtypes:
             raise TypeError("Invalid dtype")
 
-        if copy:
-            data = column.as_column(data).copy()
         kwargs = _setdefault_name(data, name=name)
-        if isinstance(data, np.ndarray) and data.dtype.kind == "M":
-            data = column.as_column(data)
-        elif isinstance(data, pd.DatetimeIndex):
-            data = column.as_column(data.values)
-        elif isinstance(data, (list, tuple)):
-            data = column.as_column(np.array(data, dtype=dtype))
+        data = column.as_column(data, dtype=dtype)
+
+        if copy:
+            data = data.copy()
+
         super().__init__(data, **kwargs)
 
     @property  # type: ignore
@@ -2263,15 +2260,18 @@ def __init__(
                 "dtype parameter is supported"
             )
 
-        if copy:
-            data = column.as_column(data).copy()
+        valid_dtypes = tuple(
+            f"timedelta64[{res}]" for res in ("s", "ms", "us", "ns")
+        )
+        if dtype not in valid_dtypes:
+            raise TypeError("Invalid dtype")
+
         kwargs = _setdefault_name(data, name=name)
-        if isinstance(data, np.ndarray) and data.dtype.kind == "m":
-            data = column.as_column(data)
-        elif isinstance(data, pd.TimedeltaIndex):
-            data = column.as_column(data.values)
-        elif isinstance(data, (list, tuple)):
-            data = column.as_column(np.array(data, dtype=dtype))
+        data = column.as_column(data, dtype=dtype)
+
+        if copy:
+            data = data.copy()
+
         super().__init__(data, **kwargs)
 
     @_cudf_nvtx_annotate
diff --git a/python/cudf/cudf/tests/test_datetime.py b/python/cudf/cudf/tests/test_datetime.py
index 07242ea49f5..04ff5b88214 100644
--- a/python/cudf/cudf/tests/test_datetime.py
+++ b/python/cudf/cudf/tests/test_datetime.py
@@ -2007,3 +2007,31 @@ def test_last(idx, offset):
     got = g.last(offset=offset)
 
     assert_eq(expect, got)
+
+
+@pytest.mark.parametrize(
+    "data",
+    [
+        [
+            "2020-01-31",
+            "2020-02-15",
+            "2020-02-29",
+            "2020-03-15",
+            "2020-03-31",
+            "2020-04-15",
+            "2020-04-30",
+        ],
+        [43534, 43543, 37897, 2000],
+    ],
+)
+@pytest.mark.parametrize("dtype", [None, "datetime64[ns]"])
+def test_datetime_constructor(data, dtype):
+    expected = pd.DatetimeIndex(data=data, dtype=dtype)
+    actual = cudf.DatetimeIndex(data=data, dtype=dtype)
+
+    assert_eq(expected, actual)
+
+    expected = pd.DatetimeIndex(data=pd.Series(data), dtype=dtype)
+    actual = cudf.DatetimeIndex(data=cudf.Series(data), dtype=dtype)
+
+    assert_eq(expected, actual)
diff --git a/python/cudf/cudf/tests/test_timedelta.py b/python/cudf/cudf/tests/test_timedelta.py
index cce2ac639ef..23270875a92 100644
--- a/python/cudf/cudf/tests/test_timedelta.py
+++ b/python/cudf/cudf/tests/test_timedelta.py
@@ -1389,3 +1389,17 @@ def test_create_TimedeltaIndex(dtype, name):
     )
     pdi = gdi.to_pandas()
     assert_eq(pdi, gdi)
+
+
+@pytest.mark.parametrize("data", [[43534, 43543, 37897, 2000]])
+@pytest.mark.parametrize("dtype", ["timedelta64[ns]"])
+def test_timedelta_constructor(data, dtype):
+    expected = pd.TimedeltaIndex(data=data, dtype=dtype)
+    actual = cudf.TimedeltaIndex(data=data, dtype=dtype)
+
+    assert_eq(expected, actual)
+
+    expected = pd.TimedeltaIndex(data=pd.Series(data), dtype=dtype)
+    actual = cudf.TimedeltaIndex(data=cudf.Series(data), dtype=dtype)
+
+    assert_eq(expected, actual)