diff --git a/pyathena/sqlalchemy/types.py b/pyathena/sqlalchemy/types.py
index 89c6a4b0..906b6c16 100644
--- a/pyathena/sqlalchemy/types.py
+++ b/pyathena/sqlalchemy/types.py
@@ -79,8 +79,10 @@ class AthenaDate(TypeEngine[date]):
     render_bind_cast = True
 
     @staticmethod
-    def process(value: date | datetime | Any) -> str:
-        if isinstance(value, (date, datetime)):
+    def process(value: date | Any) -> str:
+        # datetime is a subclass of date, so this branch also covers datetime,
+        # which is truncated to its date part.
+        if isinstance(value, date):
             return f"DATE '{value:%Y-%m-%d}'"
         return f"DATE '{value!s}'"
 
diff --git a/tests/pyathena/sqlalchemy/test_types.py b/tests/pyathena/sqlalchemy/test_types.py
index 9a4f3943..3eb9c10c 100644
--- a/tests/pyathena/sqlalchemy/test_types.py
+++ b/tests/pyathena/sqlalchemy/test_types.py
@@ -12,6 +12,7 @@
     AthenaDate,
     AthenaMap,
     AthenaStruct,
+    AthenaTimestamp,
     get_double_type,
 )
 
@@ -178,3 +179,32 @@ class TestAthenaDate:
     )
     def test_process_renders_date_only_literal(self, value, expected):
         assert AthenaDate.process(value) == expected
+
+    def test_process_falls_back_to_str(self):
+        assert AthenaDate.process("2017-01-01") == "DATE '2017-01-01'"
+
+
+class TestAthenaTimestamp:
+    @pytest.mark.parametrize(
+        ("value", "expected"),
+        [
+            # Athena TIMESTAMP has millisecond precision, so the six digits
+            # strftime("%f") emits are truncated to three.
+            (
+                datetime(2017, 1, 1, 12, 34, 56, 789012),
+                "TIMESTAMP '2017-01-01 12:34:56.789'",
+            ),
+            (
+                datetime(2017, 1, 1, 12, 34, 56),
+                "TIMESTAMP '2017-01-01 12:34:56.000'",
+            ),
+        ],
+    )
+    def test_process_renders_millisecond_precision_literal(self, value, expected):
+        assert AthenaTimestamp.process(value) == expected
+
+    def test_process_falls_back_to_str(self):
+        assert (
+            AthenaTimestamp.process("2017-01-01 12:34:56.789")
+            == "TIMESTAMP '2017-01-01 12:34:56.789'"
+        )