Index: src/wp-login.php
===================================================================
--- src/wp-login.php	(revision 53136)
+++ src/wp-login.php	(working copy)
@@ -261,7 +261,7 @@
 			 *
 			 * @param string $messages Login messages.
 			 */
-			echo '<p class="message">' . apply_filters( 'login_messages', $messages ) . "</p>\n";
+			echo '<p class="message" id="login-message">' . apply_filters( 'login_messages', $messages ) . "</p>\n";
 		}
 	}
 } // End of login_header().
@@ -1385,10 +1385,15 @@
 
 		$rememberme = ! empty( $_POST['rememberme'] );
 
-		if ( $errors->has_errors() ) {
-			$aria_describedby_error = ' aria-describedby="login_error"';
-		} else {
-			$aria_describedby_error = '';
+		$aria_describedby = '';
+		$has_errors       = $errors->has_errors();
+
+		if ( $has_errors ) {
+			$aria_describedby = ' aria-describedby="login_error"';
+ 		}
+
+		if ( $has_errors && 'message' === $errors->get_error_data() ) {
+			$aria_describedby = ' aria-describedby="login-message"';
 		}
 
 		wp_enqueue_script( 'user-profile' );
@@ -1397,13 +1402,13 @@
 		<form name="loginform" id="loginform" action="<?php echo esc_url( site_url( 'wp-login.php', 'login_post' ) ); ?>" method="post">
 			<p>
 				<label for="user_login"><?php _e( 'Username or Email Address' ); ?></label>
-				<input type="text" name="log" id="user_login"<?php echo $aria_describedby_error; ?> class="input" value="<?php echo esc_attr( $user_login ); ?>" size="20" autocapitalize="off" autocomplete="username" />
+				<input type="text" name="log" id="user_login"<?php echo $aria_describedby; ?> class="input" value="<?php echo esc_attr( $user_login ); ?>" size="20" autocapitalize="off" autocomplete="username" />
 			</p>
 
 			<div class="user-pass-wrap">
 				<label for="user_pass"><?php _e( 'Password' ); ?></label>
 				<div class="wp-pwd">
-					<input type="password" name="pwd" id="user_pass"<?php echo $aria_describedby_error; ?> class="input password-input" value="" size="20" autocomplete="current-password" />
+					<input type="password" name="pwd" id="user_pass"<?php echo $aria_describedby; ?> class="input password-input" value="" size="20" autocomplete="current-password" />
 					<button type="button" class="button button-secondary wp-hide-pw hide-if-no-js" data-toggle="0" aria-label="<?php esc_attr_e( 'Show password' ); ?>">
 						<span class="dashicons dashicons-visibility" aria-hidden="true"></span>
 					</button>