diff --git a/litellm/router.py b/litellm/router.py
index 50b39b3997..94186590bb 100644
--- a/litellm/router.py
+++ b/litellm/router.py
@@ -3037,14 +3037,42 @@ class Router:
         self,
         original_function: Callable,
         call_type: Literal[
-            "assistants", "moderation", "anthropic_messages", "responses", "aresponses"
+            "assistants",
+            "moderation",
+            "anthropic_messages",
+            "aresponses",
+            "responses",
         ] = "assistants",
     ):
-        async def new_function(
+        """
+        Creates appropriate wrapper functions for different API call types.
+
+        Returns:
+            - A synchronous function for synchronous call types
+            - An asynchronous function for asynchronous call types
+        """
+        # Handle synchronous call types
+        if call_type == "responses":
+
+            def sync_wrapper(
+                custom_llm_provider: Optional[
+                    Literal["openai", "azure", "anthropic"]
+                ] = None,
+                client: Optional[Any] = None,
+                **kwargs,
+            ):
+                return self._generic_api_call_with_fallbacks(
+                    original_function=original_function, **kwargs
+                )
+
+            return sync_wrapper
+
+        # Handle asynchronous call types
+        async def async_wrapper(
             custom_llm_provider: Optional[
                 Literal["openai", "azure", "anthropic"]
             ] = None,
-            client: Optional["AsyncOpenAI"] = None,
+            client: Optional[Any] = None,
             **kwargs,
         ):
             if call_type == "assistants":
@@ -3055,18 +3083,16 @@ class Router:
                     **kwargs,
                 )
             elif call_type == "moderation":
-
-                return await self._pass_through_moderation_endpoint_factory(  # type: ignore
-                    original_function=original_function,
-                    **kwargs,
+                return await self._pass_through_moderation_endpoint_factory(
+                    original_function=original_function, **kwargs
                 )
-            elif call_type == "anthropic_messages":
-                return await self._ageneric_api_call_with_fallbacks(  # type: ignore
+            elif call_type in ("anthropic_messages", "aresponses"):
+                return await self._ageneric_api_call_with_fallbacks(
                     original_function=original_function,
                     **kwargs,
                 )
 
-        return new_function
+        return async_wrapper
 
     async def _pass_through_assistants_endpoint_factory(
         self,