diff --git a/cosmos/airflow/graph.py b/cosmos/airflow/graph.py
index f96d3ba2a..d3466ea16 100644
--- a/cosmos/airflow/graph.py
+++ b/cosmos/airflow/graph.py
@@ -270,6 +270,7 @@ def create_task_metadata(
         }
 
         if test_behavior == TestBehavior.BUILD and node.resource_type in SUPPORTED_BUILD_RESOURCES:
+            args["on_warning_callback"] = on_warning_callback
             exclude_detached_tests_if_needed(node, args, detached_from_parent)
             task_id, args = _get_task_id_and_args(
                 node, args, use_task_group, normalize_task_id, "build", include_resource_type=True
diff --git a/cosmos/operators/local.py b/cosmos/operators/local.py
index 21fa6ae91..af64fa13a 100644
--- a/cosmos/operators/local.py
+++ b/cosmos/operators/local.py
@@ -762,8 +762,36 @@ class DbtBuildLocalOperator(DbtBuildMixin, DbtLocalBaseOperator):
 
     template_fields: Sequence[str] = DbtLocalBaseOperator.template_fields + DbtBuildMixin.template_fields  # type: ignore[operator]
 
-    def __init__(self, *args: Any, **kwargs: Any) -> None:
+    def __init__(self, *args: Any, on_warning_callback: Callable[..., Any] | None = None, **kwargs: Any) -> None:
         super().__init__(*args, **kwargs)
+        self.on_warning_callback = on_warning_callback
+        self.extract_issues: Callable[..., tuple[list[str], list[str]]]
+
+    def _handle_warnings(self, result: FullOutputSubprocessResult | dbtRunnerResult, context: Context) -> None:
+        """
+         Handles warnings by extracting log issues, creating additional context, and calling the
+         on_warning_callback with the updated context.
+
+        :param result: The result object from the build and run command.
+        :param context: The original airflow context in which the build and run command was executed.
+        """
+        if self.invocation_mode == InvocationMode.SUBPROCESS:
+            self.extract_issues = extract_freshness_warn_msg
+        elif self.invocation_mode == InvocationMode.DBT_RUNNER:
+            self.extract_issues = dbt_runner.extract_message_by_status
+
+        test_names, test_results = self.extract_issues(result)
+
+        warning_context = dict(context)
+        warning_context["test_names"] = test_names
+        warning_context["test_results"] = test_results
+
+        self.on_warning_callback and self.on_warning_callback(warning_context)
+
+    def execute(self, context: Context, **kwargs: Any) -> None:
+        result = self.build_and_run_cmd(context=context, cmd_flags=self.add_cmd_flags())
+        if self.on_warning_callback:
+            self._handle_warnings(result, context)
 
 
 class DbtLSLocalOperator(DbtLSMixin, DbtLocalBaseOperator):
diff --git a/tests/operators/test_local.py b/tests/operators/test_local.py
index 3bcd78616..a721cd858 100644
--- a/tests/operators/test_local.py
+++ b/tests/operators/test_local.py
@@ -664,7 +664,17 @@ def test_run_test_operator_with_callback(invocation_mode, failing_test_dbt_proje
             on_warning_callback=on_warning_callback,
             invocation_mode=invocation_mode,
         )
-        run_operator >> test_operator
+
+        build_operator = DbtBuildLocalOperator(
+            profile_config=mini_profile_config,
+            project_dir=failing_test_dbt_project,
+            task_id="build",
+            append_env=True,
+            on_warning_callback=on_warning_callback,
+            invocation_mode=invocation_mode,
+        )
+
+        run_operator >> build_operator >> test_operator
     run_test_dag(dag)
     assert on_warning_callback.called