diff --git a/httpcore/_async/connection_pool.py b/httpcore/_async/connection_pool.py
index 96e973d0..19f438f1 100644
--- a/httpcore/_async/connection_pool.py
+++ b/httpcore/_async/connection_pool.py
@@ -403,7 +403,10 @@ async def __aiter__(self) -> typing.AsyncIterator[bytes]:
             async for part in self._stream:
                 yield part
         except BaseException as exc:
-            await self.aclose()
+            try:
+                await self.aclose()
+            except BaseException:
+                pass
             raise exc from None
 
     async def aclose(self) -> None:
diff --git a/httpcore/_sync/connection_pool.py b/httpcore/_sync/connection_pool.py
index 9ccfa53e..b31924f6 100644
--- a/httpcore/_sync/connection_pool.py
+++ b/httpcore/_sync/connection_pool.py
@@ -403,7 +403,10 @@ def __iter__(self) -> typing.Iterator[bytes]:
             for part in self._stream:
                 yield part
         except BaseException as exc:
-            self.close()
+            try:
+                self.close()
+            except BaseException:
+                pass
             raise exc from None
 
     def close(self) -> None: