diff --git a/starlette/background.py b/starlette/background.py
index 4aaf7ae3c..e4cbbd02b 100644
--- a/starlette/background.py
+++ b/starlette/background.py
@@ -1,6 +1,8 @@
 import sys
 import typing
 
+import anyio
+
 if sys.version_info >= (3, 10):  # pragma: no cover
     from typing import ParamSpec
 else:  # pragma: no cover
@@ -39,5 +41,7 @@ def add_task(
         self.tasks.append(task)
 
     async def __call__(self) -> None:
-        for task in self.tasks:
-            await task()
+        async with anyio.create_task_group():
+            with anyio.CancelScope(shield=True):
+                for task in self.tasks:
+                    await task()