diff --git a/src/prompt_toolkit/application/_compat.py b/src/prompt_toolkit/application/_compat.py
new file mode 100644
index 000000000..f689713d3
--- /dev/null
+++ b/src/prompt_toolkit/application/_compat.py
@@ -0,0 +1,96 @@
+from __future__ import annotations
+
+import asyncio
+import sys
+from collections.abc import Callable, Coroutine
+from typing import Any, TypeVar
+
+__all__ = ["EventLoop", "asyncio_run"]
+
+_T = TypeVar("_T")
+
+if sys.version_info >= (3, 13):
+    from asyncio import EventLoop
+elif sys.platform == "win32":
+    from asyncio import ProactorEventLoop as EventLoop
+else:
+    from asyncio import SelectorEventLoop as EventLoop
+
+if sys.version_info >= (3, 12):
+    asyncio_run = asyncio.run
+elif sys.version_info >= (3, 11):
+
+    def asyncio_run(
+        main: Coroutine[Any, Any, _T],
+        *,
+        debug: bool = False,
+        loop_factory: Callable[[], asyncio.AbstractEventLoop] | None = None,
+    ) -> _T:
+        # asyncio.run from Python 3.12
+        # https://docs.python.org/3/license.html#psf-license
+        with asyncio.Runner(debug=debug, loop_factory=loop_factory) as runner:
+            return runner.run(main)
+
+else:
+    # modified version of asyncio.run from Python 3.10 to add loop_factory kwarg
+    # https://docs.python.org/3/license.html#psf-license
+    def asyncio_run(
+        main: Coroutine[Any, Any, _T],
+        *,
+        debug: bool = False,
+        loop_factory: Callable[[], asyncio.AbstractEventLoop] | None = None,
+    ) -> _T:
+        try:
+            asyncio.get_running_loop()
+        except RuntimeError:
+            pass
+        else:
+            raise RuntimeError(
+                "asyncio.run() cannot be called from a running event loop"
+            )
+
+        if not asyncio.iscoroutine(main):
+            raise ValueError(f"a coroutine was expected, got {main!r}")
+
+        if loop_factory is None:
+            loop = asyncio.new_event_loop()
+        else:
+            loop = loop_factory()
+        try:
+            if loop_factory is None:
+                asyncio.set_event_loop(loop)
+            if debug is not None:
+                loop.set_debug(debug)
+            return loop.run_until_complete(main)
+        finally:
+            try:
+                _cancel_all_tasks(loop)
+                loop.run_until_complete(loop.shutdown_asyncgens())
+                if sys.version_info >= (3, 9):
+                    loop.run_until_complete(loop.shutdown_default_executor())
+            finally:
+                if loop_factory is None:
+                    asyncio.set_event_loop(None)
+                loop.close()
+
+    def _cancel_all_tasks(loop: asyncio.AbstractEventLoop) -> None:
+        to_cancel = asyncio.all_tasks(loop)
+        if not to_cancel:
+            return
+
+        for task in to_cancel:
+            task.cancel()
+
+        loop.run_until_complete(asyncio.gather(*to_cancel, return_exceptions=True))
+
+        for task in to_cancel:
+            if task.cancelled():
+                continue
+            if task.exception() is not None:
+                loop.call_exception_handler(
+                    {
+                        "message": "unhandled exception during asyncio.run() shutdown",
+                        "exception": task.exception(),
+                        "task": task,
+                    }
+                )
diff --git a/src/prompt_toolkit/application/application.py b/src/prompt_toolkit/application/application.py
index d93c24398..9456c327e 100644
--- a/src/prompt_toolkit/application/application.py
+++ b/src/prompt_toolkit/application/application.py
@@ -86,6 +86,7 @@
 )
 from prompt_toolkit.utils import Event, in_main_thread
 
+from ._compat import EventLoop, asyncio_run
 from .current import get_app_session, set_app
 from .run_in_terminal import in_terminal, run_in_terminal
 
@@ -971,14 +972,9 @@ def _called_from_ipython() -> bool:
                 return False
 
         if inputhook is not None:
-            # Create new event loop with given input hook and run the app.
-            # In Python 3.12, we can use asyncio.run(loop_factory=...)
-            # For now, use `run_until_complete()`.
-            loop = new_eventloop_with_inputhook(inputhook)
-            result = loop.run_until_complete(coro)
-            loop.run_until_complete(loop.shutdown_asyncgens())
-            loop.close()
-            return result
+            return asyncio_run(
+                coro, loop_factory=lambda: new_eventloop_with_inputhook(inputhook)
+            )
 
         elif _called_from_ipython():
             # workaround to make input hooks work for IPython until
@@ -992,14 +988,14 @@ def _called_from_ipython() -> bool:
                 loop = asyncio.get_event_loop()
             except RuntimeError:
                 # No loop installed. Run like usual.
-                return asyncio.run(coro)
+                return asyncio_run(coro, loop_factory=EventLoop)
             else:
                 # Use existing loop.
                 return loop.run_until_complete(coro)
 
         else:
             # No loop installed. Run like usual.
-            return asyncio.run(coro)
+            return asyncio_run(coro, loop_factory=EventLoop)
 
     def _handle_exception(
         self, loop: AbstractEventLoop, context: dict[str, Any]