diff --git a/tenacity/_asyncio.py b/tenacity/_asyncio.py
index 16aec620..27c26642 100644
--- a/tenacity/_asyncio.py
+++ b/tenacity/_asyncio.py
@@ -25,6 +25,7 @@
 from tenacity import DoAttempt
 from tenacity import DoSleep
 from tenacity import RetryCallState
+from tenacity import _utils
 
 WrappedFnReturnT = t.TypeVar("WrappedFnReturnT")
 WrappedFn = t.TypeVar("WrappedFn", bound=t.Callable[..., t.Awaitable[t.Any]])
@@ -46,7 +47,7 @@ async def __call__(  # type: ignore[override]
 
         retry_state = RetryCallState(retry_object=self, fn=fn, args=args, kwargs=kwargs)
         while True:
-            do = self.iter(retry_state=retry_state)
+            do = await self.iter(retry_state=retry_state)
             if isinstance(do, DoAttempt):
                 try:
                     result = await fn(*args, **kwargs)
@@ -60,6 +61,47 @@ async def __call__(  # type: ignore[override]
             else:
                 return do  # type: ignore[no-any-return]
 
+    @classmethod
+    def _wrap_action_func(cls, fn: t.Callable[..., t.Any]) -> t.Callable[..., t.Any]:
+        if _utils.is_coroutine_callable(fn):
+            return fn
+
+        async def inner(*args: t.Any, **kwargs: t.Any) -> t.Any:
+            return fn(*args, **kwargs)
+
+        return inner
+
+    def _add_action_func(self, fn: t.Callable[..., t.Any]) -> None:
+        self.iter_state.actions.append(self._wrap_action_func(fn))
+
+    async def _run_retry(self, retry_state: "RetryCallState") -> None:  # type: ignore[override]
+        self.iter_state.retry_run_result = await self._wrap_action_func(self.retry)(
+            retry_state
+        )
+
+    async def _run_wait(self, retry_state: "RetryCallState") -> None:  # type: ignore[override]
+        if self.wait:
+            sleep = await self._wrap_action_func(self.wait)(retry_state)
+        else:
+            sleep = 0.0
+
+        retry_state.upcoming_sleep = sleep
+
+    async def _run_stop(self, retry_state: "RetryCallState") -> None:  # type: ignore[override]
+        self.statistics["delay_since_first_attempt"] = retry_state.seconds_since_start
+        self.iter_state.stop_run_result = await self._wrap_action_func(self.stop)(
+            retry_state
+        )
+
+    async def iter(
+        self, retry_state: "RetryCallState"
+    ) -> t.Union[DoAttempt, DoSleep, t.Any]:  # noqa: A003
+        self._begin_iter(retry_state)
+        result = None
+        for action in self.iter_state.actions:
+            result = await action(retry_state)
+        return result
+
     def __iter__(self) -> t.Generator[AttemptManager, None, None]:
         raise TypeError("AsyncRetrying object is not iterable")
 
@@ -70,7 +112,7 @@ def __aiter__(self) -> "AsyncRetrying":
 
     async def __anext__(self) -> AttemptManager:
         while True:
-            do = self.iter(retry_state=self._retry_state)
+            do = await self.iter(retry_state=self._retry_state)
             if do is None:
                 raise StopAsyncIteration
             elif isinstance(do, DoAttempt):
diff --git a/tenacity/_utils.py b/tenacity/_utils.py
index 67ee0dea..4e34115e 100644
--- a/tenacity/_utils.py
+++ b/tenacity/_utils.py
@@ -13,7 +13,8 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-
+import functools
+import inspect
 import sys
 import typing
 from datetime import timedelta
@@ -76,3 +77,13 @@ def to_seconds(time_unit: time_unit_type) -> float:
     return float(
         time_unit.total_seconds() if isinstance(time_unit, timedelta) else time_unit
     )
+
+
+def is_coroutine_callable(call: typing.Callable[..., typing.Any]) -> bool:
+    if inspect.isclass(call):
+        return False
+    if inspect.iscoroutinefunction(call):
+        return True
+    partial_call = isinstance(call, functools.partial) and call.func
+    dunder_call = partial_call or getattr(call, "__call__", None)
+    return inspect.iscoroutinefunction(dunder_call)
diff --git a/tests/test_utils.py b/tests/test_utils.py
new file mode 100644
index 00000000..ec7b3ee5
--- /dev/null
+++ b/tests/test_utils.py
@@ -0,0 +1,41 @@
+import functools
+
+from tenacity import _utils
+
+
+def test_is_coroutine_callable() -> None:
+    async def async_func() -> None:
+        pass
+
+    def sync_func() -> None:
+        pass
+
+    class AsyncClass:
+        async def __call__(self) -> None:
+            pass
+
+    class SyncClass:
+        def __call__(self) -> None:
+            pass
+
+    lambda_fn = lambda: None  # noqa: E731
+
+    partial_async_func = functools.partial(async_func)
+    partial_sync_func = functools.partial(sync_func)
+    partial_async_class = functools.partial(AsyncClass().__call__)
+    partial_sync_class = functools.partial(SyncClass().__call__)
+    partial_lambda_fn = functools.partial(lambda_fn)
+
+    assert _utils.is_coroutine_callable(async_func) is True
+    assert _utils.is_coroutine_callable(sync_func) is False
+    assert _utils.is_coroutine_callable(AsyncClass) is False
+    assert _utils.is_coroutine_callable(AsyncClass()) is True
+    assert _utils.is_coroutine_callable(SyncClass) is False
+    assert _utils.is_coroutine_callable(SyncClass()) is False
+    assert _utils.is_coroutine_callable(lambda_fn) is False
+
+    assert _utils.is_coroutine_callable(partial_async_func) is True
+    assert _utils.is_coroutine_callable(partial_sync_func) is False
+    assert _utils.is_coroutine_callable(partial_async_class) is True
+    assert _utils.is_coroutine_callable(partial_sync_class) is False
+    assert _utils.is_coroutine_callable(partial_lambda_fn) is False