diff --git a/pandas/_libs/index.pyx b/pandas/_libs/index.pyx
index ba2838d59f814..7000c07b1f5a6 100644
--- a/pandas/_libs/index.pyx
+++ b/pandas/_libs/index.pyx
@@ -544,6 +544,10 @@ cpdef convert_scalar(ndarray arr, object value):
             pass
         elif isinstance(value, timedelta):
             return Timedelta(value).value
+        elif util.is_datetime64_object(value):
+            # exclude np.datetime64("NaT") which would otherwise be picked up
+            #  by the `value != value check below
+            pass
         elif value is None or value != value:
             return NPY_NAT
         elif isinstance(value, str):
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 6a58b1ea6f82d..dc9a42b7071cb 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -46,6 +46,7 @@
     ABCSparseSeries,
 )
 from pandas.core.dtypes.missing import (
+    is_valid_nat_for_dtype,
     isna,
     na_value_for_dtype,
     notna,
@@ -1198,13 +1199,15 @@ def setitem(key, value):
                     pass
                 elif is_timedelta64_dtype(self.dtype):
                     # reassign a null value to iNaT
-                    if isna(value):
+                    if is_valid_nat_for_dtype(value, self.dtype):
+                        # exclude np.datetime64("NaT")
                         value = iNaT
 
                         try:
                             self.index._engine.set_value(self._values, key, value)
                             return
-                        except TypeError:
+                        except (TypeError, ValueError):
+                            # ValueError appears in only some builds in CI
                             pass
 
                 self.loc[key] = value
diff --git a/pandas/tests/series/indexing/test_indexing.py b/pandas/tests/series/indexing/test_indexing.py
index 6ff878f07da84..d73be76795c88 100644
--- a/pandas/tests/series/indexing/test_indexing.py
+++ b/pandas/tests/series/indexing/test_indexing.py
@@ -654,6 +654,36 @@ def test_timedelta_assignment():
     tm.assert_series_equal(s, expected)
 
 
+@pytest.mark.parametrize(
+    "nat_val,should_cast",
+    [
+        (pd.NaT, True),
+        (np.timedelta64("NaT", "ns"), True),
+        (np.datetime64("NaT", "ns"), False),
+    ],
+)
+def test_td64_series_assign_nat(nat_val, should_cast):
+    # some nat-like values should be cast to timedelta64 when inserting
+    #  into a timedelta64 series.  Others should coerce to object
+    #  and retain their dtypes.
+    base = pd.Series([0, 1, 2], dtype="m8[ns]")
+    expected = pd.Series([pd.NaT, 1, 2], dtype="m8[ns]")
+    if not should_cast:
+        expected = expected.astype(object)
+
+    ser = base.copy(deep=True)
+    ser[0] = nat_val
+    tm.assert_series_equal(ser, expected)
+
+    ser = base.copy(deep=True)
+    ser.loc[0] = nat_val
+    tm.assert_series_equal(ser, expected)
+
+    ser = base.copy(deep=True)
+    ser.iloc[0] = nat_val
+    tm.assert_series_equal(ser, expected)
+
+
 @pytest.mark.parametrize(
     "td",
     [