diff --git a/glib/gspawn.c b/glib/gspawn.c
index fa3cfe7c0..9b503cf7b 100644
--- a/glib/gspawn.c
+++ b/glib/gspawn.c
@@ -1330,12 +1330,17 @@ safe_closefrom (int lowfd)
    * simple wrapper of the fcntl command.
    */
   (void) fcntl (lowfd, F_CLOSEM);
-#elif defined(HAVE_CLOSE_RANGE)
+#else
+
+#if defined(HAVE_CLOSE_RANGE)
   /* close_range() is available in Linux since kernel 5.9, and on FreeBSD at
    * around the same time. It was designed for use in async-signal-safe
-   * situations: https://bugs.python.org/issue38061 */
-  (void) close_range (lowfd, G_MAXUINT);
-#else
+   * situations: https://bugs.python.org/issue38061
+   *
+   * Handle ENOSYS in case it’s supported in libc but not the kernel; if so,
+   * fall back to safe_fdwalk(). */
+  if (close_range (lowfd, G_MAXUINT) != 0 && errno == ENOSYS)
+#endif  /* HAVE_CLOSE_RANGE */
   (void) safe_fdwalk (close_func, GINT_TO_POINTER (lowfd));
 #endif
 }