diff --git a/taipy/gui/_renderers/builder.py b/taipy/gui/_renderers/builder.py
index 799b12da53..bd84bdfd4c 100644
--- a/taipy/gui/_renderers/builder.py
+++ b/taipy/gui/_renderers/builder.py
@@ -171,7 +171,7 @@ def _get_variable_hash_names(
                 if _is_function(val) and not hash_name:
                     # if it's not a callable (and not a string), forget it
                     if _is_unnamed_function(val):
-                        # lambda or callable instance
+                        # lambda, inner function or callable instance
                         hash_name = _get_lambda_id(t.cast(LambdaType, val))
                         gui._bind_var_val(hash_name, val)  # type: ignore[arg-type]
                     else:
diff --git a/taipy/gui/builder/_element.py b/taipy/gui/builder/_element.py
index dafba96694..72c9af724c 100644
--- a/taipy/gui/builder/_element.py
+++ b/taipy/gui/builder/_element.py
@@ -108,7 +108,7 @@ def _parse_property(self, key: str, value: t.Any) -> t.Any:
             return value
         if isinstance(value, FunctionType):
             if key.startswith("on_") or self._is_callable(key):
-                return value if value.__name__.startswith("<") else value.__name__
+                return value if "<" in value.__qualname__ else value.__name__
             # Parse lambda function_is_callable
             if (lambda_call := self.__parse_lambda_property(key, value)) is not None:
                 return lambda_call
diff --git a/taipy/gui/utils/callable.py b/taipy/gui/utils/callable.py
index 40586f3c6a..c3b31e99b1 100644
--- a/taipy/gui/utils/callable.py
+++ b/taipy/gui/utils/callable.py
@@ -27,4 +27,8 @@ def _function_name(s: t.Any) -> str:
 
 
 def _is_unnamed_function(s: t.Any):
-    return (hasattr(s, "__name__") and s.__name__ == "<lambda>") or (callable(s) and not hasattr(s, "__name__"))
+    return (
+        (hasattr(s, "__name__") and s.__name__ == "<lambda>")
+        or (callable(s) and not hasattr(s, "__name__"))
+        or (hasattr(s, "__qualname__") and "<locals>" in s.__qualname__)
+    )
diff --git a/tests/gui/actions/test_download.py b/tests/gui/actions/test_download.py
index 686366a904..1e2c4c05d7 100644
--- a/tests/gui/actions/test_download.py
+++ b/tests/gui/actions/test_download.py
@@ -64,8 +64,9 @@ def on_download_action(state: State):
     helpers.assert_outward_ws_simple_message(
         received_messages[0],
         "DF",
-        {"name": "filename.txt", "context": "test_download", "onAction": "tp_on_download_action_0"},
+        {"name": "filename.txt", "context": "test_download"},
     )
+    assert "onAction" in received_messages[0]["args"] # inner function is treated as lambda
 
 
 def test_bad_download(gui: Gui, helpers):
diff --git a/tests/gui/builder/test_on_action.py b/tests/gui/builder/test_on_action.py
index 6de3502651..997f19f7cc 100644
--- a/tests/gui/builder/test_on_action.py
+++ b/tests/gui/builder/test_on_action.py
@@ -19,7 +19,7 @@ def on_slider(state):
     gui._bind_var_val("on_slider", on_slider)
     with tgb.Page(frame=None) as page:
         tgb.slider(value="{value}", on_change=on_slider)  # type: ignore[attr-defined] # noqa: B023
-    expected_list = ['<Slider','onChange="on_slider"']
+    expected_list = ['<Slider','onChange="__lambda_'] # inner function is treated as lambda
     helpers.test_control_builder(gui, page, expected_list)