diff --git a/docs/versionhistory.rst b/docs/versionhistory.rst
index fb81ec05..bdf0922a 100644
--- a/docs/versionhistory.rst
+++ b/docs/versionhistory.rst
@@ -12,6 +12,9 @@ This library adheres to `Semantic Versioning 2.0 <http://semver.org/>`_.
   when cancelling a task in a TaskGroup created with the ``start()`` method before
   the first checkpoint is reached after calling ``task_status.started()``
   (`#706 <https://github.com/agronholm/anyio/issues/706>`_; PR by Dominik Schwabe)
+- Fixed cancellation delivery on asyncio incrementing the wrong cancel scope's
+  cancellation counter when cascading a cancel operation to a child scope, thus failing
+  to uncancel the host task (`#716 <https://github.com/agronholm/anyio/issues/716>`_)
 - Fixed erroneous ``TypedAttributeLookupError`` if a typed attribute getter raises
   ``KeyError``
 - Fixed the asyncio backend not respecting the ``PYTHONASYNCIODEBUG`` environment
diff --git a/src/anyio/_backends/_asyncio.py b/src/anyio/_backends/_asyncio.py
index 860c9999..ecd865a7 100644
--- a/src/anyio/_backends/_asyncio.py
+++ b/src/anyio/_backends/_asyncio.py
@@ -488,7 +488,7 @@ def _deliver_cancellation(self, origin: CancelScope) -> bool:
             if task is not current and (task is self._host_task or _task_started(task)):
                 waiter = task._fut_waiter  # type: ignore[attr-defined]
                 if not isinstance(waiter, asyncio.Future) or not waiter.done():
-                    self._cancel_calls += 1
+                    origin._cancel_calls += 1
                     if sys.version_info >= (3, 9):
                         task.cancel(f"Cancelled by cancel scope {id(origin):x}")
                     else:
diff --git a/tests/test_taskgroups.py b/tests/test_taskgroups.py
index d54115f4..da84f656 100644
--- a/tests/test_taskgroups.py
+++ b/tests/test_taskgroups.py
@@ -458,6 +458,19 @@ async def test_cancel_before_entering_scope() -> None:
         pytest.fail("execution should not reach this point")
 
 
+@pytest.mark.xfail(
+    sys.version_info < (3, 11), reason="Requires asyncio.Task.cancelling()"
+)
+@pytest.mark.parametrize("anyio_backend", ["asyncio"])
+async def test_cancel_counter_nested_scopes() -> None:
+    with CancelScope() as root_scope:
+        with CancelScope():
+            root_scope.cancel()
+            await sleep(0.5)
+
+    assert not cast(asyncio.Task, asyncio.current_task()).cancelling()
+
+
 async def test_exception_group_children() -> None:
     with pytest.raises(BaseExceptionGroup) as exc:
         async with create_task_group() as tg: