diff --git a/src/quart/wrappers/response.py b/src/quart/wrappers/response.py
index 065eabf..a63bcdf 100644
--- a/src/quart/wrappers/response.py
+++ b/src/quart/wrappers/response.py
@@ -102,19 +102,24 @@ async def __anext__(self) -> bytes:
 
 
 class IterableBody(ResponseBody):
-    def __init__(self, iterable: AsyncGenerator[bytes, None] | Iterable) -> None:
+    def __init__(self, iterable: AsyncIterable[bytes] | Iterable) -> None:
         self.iter: AsyncGenerator[bytes, None]
         if isasyncgen(iterable):
             self.iter = iterable
         elif isgenerator(iterable):
             self.iter = run_sync_iterable(iterable)
-        else:
-
+        elif isinstance(iterable, AsyncIterable):
             async def _aiter() -> AsyncGenerator[bytes, None]:
-                for data in iterable:  # type: ignore
+                async for data in iterable:
                     yield data
-
             self.iter = _aiter()
+        elif isinstance(iterable, Iterable):
+            async def _aiter() -> AsyncGenerator[bytes, None]:
+                for data in iterable:
+                    yield data
+            self.iter = _aiter()
+        else:
+            raise ValueError("unreachable?")
 
     async def __aenter__(self) -> IterableBody:
         return self
@@ -262,7 +267,7 @@ class Response(SansIOResponse):
 
     def __init__(
         self,
-        response: ResponseBody | AnyStr | Iterable | None = None,
+        response: ResponseBody | AnyStr | Iterable | AsyncIterable | None = None,
         status: int | None = None,
         headers: dict | Headers | None = None,
         mimetype: str | None = None,