diff --git a/src/wp-includes/functions.php b/src/wp-includes/functions.php
index bece4e7914..951020d387 100644
--- a/src/wp-includes/functions.php
+++ b/src/wp-includes/functions.php
@@ -1582,6 +1582,8 @@ function do_feed_atom( $for_comments ) {
  * Displays the default robots.txt file content.
  *
  * @since 2.1.0
+ * @since 5.3.0 Remove the "Disallow: /" output if search engine visiblity is
+ *              discouraged in favor of robots meta HTML tag in wp_no_robots().
  */
 function do_robots() {
 	header( 'Content-Type: text/plain; charset=utf-8' );
@@ -1595,14 +1597,11 @@ function do_robots() {
 
 	$output = "User-agent: *\n";
 	$public = get_option( 'blog_public' );
-	if ( '0' == $public ) {
-		$output .= "Disallow: /\n";
-	} else {
-		$site_url = parse_url( site_url() );
-		$path     = ( ! empty( $site_url['path'] ) ) ? $site_url['path'] : '';
-		$output  .= "Disallow: $path/wp-admin/\n";
-		$output  .= "Allow: $path/wp-admin/admin-ajax.php\n";
-	}
+
+	$site_url = parse_url( site_url() );
+	$path     = ( ! empty( $site_url['path'] ) ) ? $site_url['path'] : '';
+	$output  .= "Disallow: $path/wp-admin/\n";
+	$output  .= "Allow: $path/wp-admin/admin-ajax.php\n";
 
 	/**
 	 * Filters the robots.txt output.
diff --git a/src/wp-includes/general-template.php b/src/wp-includes/general-template.php
index d6bcc019b1..614853860f 100644
--- a/src/wp-includes/general-template.php
+++ b/src/wp-includes/general-template.php
@@ -2986,12 +2986,18 @@ function noindex() {
  * Display a noindex meta tag.
  *
  * Outputs a noindex meta tag that tells web robots not to index the page content.
- * Typical usage is as a wp_head callback. add_action( 'wp_head', 'wp_no_robots' );
+ * Typical usage is as a {@see 'wp_head'} callback. add_action( 'wp_head', 'wp_no_robots' );
  *
  * @since 3.3.0
+ * @since 5.3.0 Echo "noindex,nofollow" if search engine visibility is discouraged.
  */
 function wp_no_robots() {
-	echo "<meta name='robots' content='noindex,follow' />\n";
+	if ( get_option( 'blog_public' ) ) {
+		echo "<meta name='robots' content='noindex,follow' />\n";
+		return;
+	}
+
+	echo "<meta name='robots' content='noindex,nofollow' />\n";
 }
 
 /**
diff --git a/tests/phpunit/tests/general/template.php b/tests/phpunit/tests/general/template.php
index daa77da5b9..fa6636170c 100644
--- a/tests/phpunit/tests/general/template.php
+++ b/tests/phpunit/tests/general/template.php
@@ -612,4 +612,19 @@ class Tests_General_Template extends WP_UnitTestCase {
 
 		$this->assertSame( $expected, $result );
 	}
+
+	/**
+	 * @ticket 43590
+	 */
+	function test_wp_no_robots() {
+		// Simulate private site (search engines discouraged).
+		update_option( 'blog_public', '0' );
+		$actual_private = get_echo( 'wp_no_robots' );
+		$this->assertSame( "<meta name='robots' content='noindex,nofollow' />\n", $actual_private );
+
+		// Simulate public site.
+		update_option( 'blog_public', '1' );
+		$actual_public = get_echo( 'wp_no_robots' );
+		$this->assertSame( "<meta name='robots' content='noindex,follow' />\n", $actual_public );
+	}
 }