diff --git a/libgomp/plugin/plugin-nvptx.c b/libgomp/plugin/plugin-nvptx.c
index 6033c71a9db..ec103a2f40b 100644
--- a/libgomp/plugin/plugin-nvptx.c
+++ b/libgomp/plugin/plugin-nvptx.c
@@ -1931,9 +1931,4 @@ GOMP_OFFLOAD_run (int ord, void *tgt_fn, void *tgt_vars, void **args)
   nvptx_stacks_free (stacks, teams * threads);
 }
 
-void
-GOMP_OFFLOAD_async_run (int ord, void *tgt_fn, void *tgt_vars, void **args,
-			void *async_data)
-{
-  GOMP_PLUGIN_fatal ("GOMP_OFFLOAD_async_run unimplemented");
-}
+/* TODO: Implement GOMP_OFFLOAD_async_run. */
diff --git a/libgomp/target.c b/libgomp/target.c
index 3df007283f4..0ff727de47d 100644
--- a/libgomp/target.c
+++ b/libgomp/target.c
@@ -2022,6 +2022,16 @@ GOMP_target (int device, void (*fn) (void *), const void *unused,
   gomp_unmap_vars (tgt_vars, true);
 }
 
+static inline unsigned int
+clear_unsupported_flags (struct gomp_device_descr *devicep, unsigned int flags)
+{
+  /* If we cannot run asynchronously, simply ignore nowait.  */
+  if (devicep != NULL && devicep->async_run_func == NULL)
+    flags &= ~GOMP_TARGET_FLAG_NOWAIT;
+
+  return flags;
+}
+
 /* Like GOMP_target, but KINDS is 16-bit, UNUSED is no longer present,
    and several arguments have been added:
    FLAGS is a bitmask, see GOMP_TARGET_FLAG_* in gomp-constants.h.
@@ -2054,6 +2064,8 @@ GOMP_target_ext (int device, void (*fn) (void *), size_t mapnum,
   size_t tgt_align = 0, tgt_size = 0;
   bool fpc_done = false;
 
+  flags = clear_unsupported_flags (devicep, flags);
+
   if (flags & GOMP_TARGET_FLAG_NOWAIT)
     {
       struct gomp_thread *thr = gomp_thread ();
@@ -2524,6 +2536,7 @@ gomp_target_task_fn (void *data)
 	}
       ttask->state = GOMP_TARGET_TASK_READY_TO_RUN;
 
+      assert (devicep->async_run_func);
       devicep->async_run_func (devicep->target_id, fn_addr, actual_arguments,
 			       ttask->args, (void *) ttask);
       return true;
@@ -3040,7 +3053,7 @@ gomp_load_plugin_for_device (struct gomp_device_descr *device,
   if (device->capabilities & GOMP_OFFLOAD_CAP_OPENMP_400)
     {
       DLSYM (run);
-      DLSYM (async_run);
+      DLSYM_OPT (async_run, async_run);
       DLSYM_OPT (can_run, can_run);
       DLSYM (dev2dev);
     }
diff --git a/libgomp/testsuite/libgomp.c/target-33.c b/libgomp/testsuite/libgomp.c/target-33.c
index 15d2d7e38ab..1bed4b6bc67 100644
--- a/libgomp/testsuite/libgomp.c/target-33.c
+++ b/libgomp/testsuite/libgomp.c/target-33.c
@@ -1,6 +1,3 @@
-/* { dg-xfail-run-if "GOMP_OFFLOAD_async_run not implemented" { offload_target_nvptx } }
-   Cf. https://gcc.gnu.org/PR81688.  */
-
 extern void abort (void);
 
 int
diff --git a/libgomp/testsuite/libgomp.c/target-34.c b/libgomp/testsuite/libgomp.c/target-34.c
index 5a3596424d8..66d9f54202b 100644
--- a/libgomp/testsuite/libgomp.c/target-34.c
+++ b/libgomp/testsuite/libgomp.c/target-34.c
@@ -1,6 +1,3 @@
-/* { dg-xfail-run-if "GOMP_OFFLOAD_async_run not implemented" { offload_target_nvptx } }
-   Cf. https://gcc.gnu.org/PR81688.  */
-
 extern void abort (void);
 
 int