diff --git a/xarray/coding/times.py b/xarray/coding/times.py
index 47f2d8ee19a..01e3bd1cf1d 100644
--- a/xarray/coding/times.py
+++ b/xarray/coding/times.py
@@ -1316,7 +1316,14 @@ def encode(self, variable: Variable, name: T_Name = None) -> Variable:
             units = encoding.pop("units", None)
             calendar = encoding.pop("calendar", None)
             dtype = encoding.pop("dtype", None)
+
+            # in the case of packed data we need to encode into
+            # float first, the correct dtype will be established
+            # via CFScaleOffsetCoder/CFMaskCoder
+            if "add_offset" in encoding or "scale_factor" in encoding:
+                dtype = data.dtype if data.dtype.kind == "f" else "float64"
             (data, units, calendar) = encode_cf_datetime(data, units, calendar, dtype)
+
             # if no dtype is provided, preserve data.dtype in encoding
             if dtype is None:
                 safe_setitem(encoding, "dtype", data.dtype, name=name)
@@ -1371,17 +1378,20 @@ def encode(self, variable: Variable, name: T_Name = None) -> Variable:
         if np.issubdtype(variable.data.dtype, np.timedelta64):
             dims, data, attrs, encoding = unpack_for_encoding(variable)
 
+            dtype = encoding.pop("dtype", None)
+
             # in the case of packed data we need to encode into
             # float first, the correct dtype will be established
             # via CFScaleOffsetCoder/CFMaskCoder
-            dtype = None
             if "add_offset" in encoding or "scale_factor" in encoding:
-                encoding.pop("dtype")
                 dtype = data.dtype if data.dtype.kind == "f" else "float64"
 
-            data, units = encode_cf_timedelta(
-                data, encoding.pop("units", None), encoding.get("dtype", dtype)
-            )
+            data, units = encode_cf_timedelta(data, encoding.pop("units", None), dtype)
+
+            # if no dtype is provided, preserve data.dtype in encoding
+            if dtype is None:
+                safe_setitem(encoding, "dtype", data.dtype, name=name)
+
             safe_setitem(attrs, "units", units, name=name)
 
             return Variable(dims, data, attrs, encoding, fastpath=True)
diff --git a/xarray/coding/variables.py b/xarray/coding/variables.py
index 72125da3332..77e2f0602ce 100644
--- a/xarray/coding/variables.py
+++ b/xarray/coding/variables.py
@@ -484,25 +484,30 @@ def decode(self, variable: Variable, name: T_Name = None):
             )
 
         if encoded_fill_values:
-            # special case DateTime to properly handle NaT
-            # we need to check if time-like will be decoded or not
-            # in further processing
             dtype: np.typing.DTypeLike
             decoded_fill_value: Any
-            is_time_like = _is_time_like(attrs.get("units"))
-            if (
-                (is_time_like == "datetime" and self.decode_times)
-                or (is_time_like == "timedelta" and self.decode_timedelta)
-            ) and data.dtype.kind in "iu":
-                dtype, decoded_fill_value = np.int64, np.iinfo(np.int64).min
+            # in case of packed data we have to decode into float
+            # in any case
+            if "scale_factor" in attrs or "add_offset" in attrs:
+                dtype, decoded_fill_value = (
+                    _choose_float_dtype(data.dtype, attrs),
+                    np.nan,
+                )
             else:
-                if "scale_factor" not in attrs and "add_offset" not in attrs:
-                    dtype, decoded_fill_value = dtypes.maybe_promote(data.dtype)
-                else:
+                # in case of no-packing special case DateTime/Timedelta to properly
+                # handle NaT, we need to check if time-like will be decoded
+                # or not in further processing
+                is_time_like = _is_time_like(attrs.get("units"))
+                if (
+                    (is_time_like == "datetime" and self.decode_times)
+                    or (is_time_like == "timedelta" and self.decode_timedelta)
+                ) and data.dtype.kind in "iu":
                     dtype, decoded_fill_value = (
-                        _choose_float_dtype(data.dtype, attrs),
-                        np.nan,
-                    )
+                        np.int64,
+                        np.iinfo(np.int64).min,
+                    )  # np.dtype(f"{is_time_like}64[s]")
+                else:
+                    dtype, decoded_fill_value = dtypes.maybe_promote(data.dtype)
 
             transform = partial(
                 _apply_mask,
diff --git a/xarray/tests/test_coding_times.py b/xarray/tests/test_coding_times.py
index 480bd96f3f4..8f031593a27 100644
--- a/xarray/tests/test_coding_times.py
+++ b/xarray/tests/test_coding_times.py
@@ -525,6 +525,24 @@ def test_decoded_cf_datetime_array_2d(time_unit: PDDatetimeUnitOptions) -> None:
     assert_array_equal(np.asarray(result), expected)
 
 
+@pytest.mark.parametrize("decode_times", [True, False])
+@pytest.mark.parametrize("mask_and_scale", [True, False])
+def test_decode_datetime_mask_and_scale(
+    decode_times: bool, mask_and_scale: bool
+) -> None:
+    attrs = {
+        "units": "nanoseconds since 1970-01-01",
+        "_FillValue": np.int16(-1),
+        "add_offset": 100000.0,
+    }
+    encoded = Variable(["time"], np.array([0, -1, 1], "int16"), attrs=attrs)
+    decoded = conventions.decode_cf_variable(
+        "foo", encoded, mask_and_scale=mask_and_scale, decode_times=decode_times
+    )
+    result = conventions.encode_cf_variable(decoded, name="foo")
+    assert_equal(encoded, result)
+
+
 FREQUENCIES_TO_ENCODING_UNITS = {
     "ns": "nanoseconds",
     "us": "microseconds",
@@ -1914,7 +1932,7 @@ def test_lazy_decode_timedelta_error() -> None:
 def test_decode_timedelta_mask_and_scale(
     decode_timedelta: bool, mask_and_scale: bool
 ) -> None:
-    attrs = {"units": "days", "_FillValue": np.int16(-1), "add_offset": 100.0}
+    attrs = {"units": "nanoseconds", "_FillValue": np.int16(-1), "add_offset": 100000.0}
     encoded = Variable(["time"], np.array([0, -1, 1], "int16"), attrs=attrs)
     decoded = conventions.decode_cf_variable(
         "foo", encoded, mask_and_scale=mask_and_scale, decode_timedelta=decode_timedelta