diff --git a/cosmos/operators/local.py b/cosmos/operators/local.py
index 4888583bb..fdf1d7d39 100644
--- a/cosmos/operators/local.py
+++ b/cosmos/operators/local.py
@@ -42,6 +42,7 @@
 )
 from cosmos.dbt.parser.output import (
     extract_log_issues,
+    parse_output,
 )
 
 logger = get_logger(__name__)
@@ -350,11 +351,12 @@ def get_openlineage_facets_on_complete(self, task_instance: TaskInstance) -> Ope
             job_facets=job_facets,
         )
 
-    def build_and_run_cmd(self, context: Context, cmd_flags: list[str] | None = None) -> None:
+    def build_and_run_cmd(self, context: Context, cmd_flags: list[str] | None = None) -> FullOutputSubprocessResult:
         dbt_cmd, env = self.build_cmd(context=context, cmd_flags=cmd_flags)
         dbt_cmd = dbt_cmd or []
         result = self.run_command(cmd=dbt_cmd, env=env, context=context)
         logger.info(result.output)
+        return result
 
     def execute(self, context: Context) -> None:
         self.build_and_run_cmd(context=context)
@@ -492,6 +494,16 @@ def _handle_warnings(self, result: FullOutputSubprocessResult, context: Context)
         if self.on_warning_callback:
             self.on_warning_callback(warning_context)
 
+    def execute(self, context: Context) -> None:
+        result = self.build_and_run_cmd(context=context)
+
+        if not self._should_run_tests(result):
+            return
+
+        warnings = parse_output(result, "WARN")
+        if warnings > 0:
+            self._handle_warnings(result, context)
+
 
 class DbtRunOperationLocalOperator(DbtLocalBaseOperator):
     """
diff --git a/tests/operators/test_local.py b/tests/operators/test_local.py
index 94b0f8e27..fdd77aec3 100644
--- a/tests/operators/test_local.py
+++ b/tests/operators/test_local.py
@@ -302,3 +302,35 @@ def test_operator_execute_without_flags(mock_build_and_run_cmd, operator_class):
     )
     task.execute(context={})
     mock_build_and_run_cmd.assert_called_once_with(context={})
+
+
+@patch("cosmos.operators.local.parse_output")
+@patch("cosmos.operators.local.DbtLocalBaseOperator.build_and_run_cmd")
+def test_test_operator_execute_with_on_warning_callback(mock_build_and_run_cmd, mock_parse_output):
+    # simulate when there is warning
+    mock_parse_output.return_value = 1
+
+    warning_handler = MagicMock()
+
+    test_operator = DbtTestLocalOperator(
+        profile_config=profile_config, project_dir="my/dir", task_id="test", on_warning_callback=warning_handler
+    )
+    test_operator.execute(context={})
+    mock_build_and_run_cmd.assert_called_once()
+    warning_handler.assert_called_once()
+
+
+@patch("cosmos.operators.local.parse_output")
+@patch("cosmos.operators.local.DbtLocalBaseOperator.build_and_run_cmd")
+def test_test_operator_execute_without_on_warning_callback(mock_build_and_run_cmd, mock_parse_output):
+    # simulate when there is no warning
+    mock_parse_output.return_value = 0
+
+    warning_handler = MagicMock()
+
+    test_operator = DbtTestLocalOperator(
+        profile_config=profile_config, project_dir="my/dir", task_id="test", on_warning_callback=warning_handler
+    )
+    test_operator.execute(context={})
+    mock_build_and_run_cmd.assert_called_once()
+    warning_handler.assert_not_called()