wp_ajax_add_menu_item

function wp_ajax_add_menu_item() {
	check_ajax_referer( 'add-menu_item', 'menu-settings-column-nonce' );

	if ( ! current_user_can( 'edit_theme_options' ) ) {
		wp_die( -1 );
	}

	require_once ABSPATH . 'wp-admin/includes/nav-menu.php';

	// For performance reasons, we omit some object properties from the checklist.
	// The following is a hacky way to restore them when adding non-custom items.
	$menu_items_data = array();

	foreach ( (array) $_POST['menu-item'] as $menu_item_data ) {
		if (
			! empty( $menu_item_data['menu-item-type'] ) &&
			'custom' !== $menu_item_data['menu-item-type'] &&
			! empty( $menu_item_data['menu-item-object-id'] )
		) {
			switch ( $menu_item_data['menu-item-type'] ) {
				case 'post_type':
					$_object = get_post( $menu_item_data['menu-item-object-id'] );
					break;

				case 'post_type_archive':
					$_object = get_post_type_object( $menu_item_data['menu-item-object'] );
					break;

				case 'taxonomy':
					$_object = get_term( $menu_item_data['menu-item-object-id'], $menu_item_data['menu-item-object'] );
					break;
			}

			$_menu_items = array_map( 'wp_setup_nav_menu_item', array( $_object ) );
			$_menu_item  = reset( $_menu_items );

			// Restore the missing menu item properties.
			$menu_item_data['menu-item-description'] = $_menu_item->description;
		}

		$menu_items_data[] = $menu_item_data;
	}

	$item_ids = wp_save_nav_menu_items( 0, $menu_items_data );
	if ( is_wp_error( $item_ids ) ) {
		wp_die( 0 );
	}

	$menu_items = array();

	foreach ( (array) $item_ids as $menu_item_id ) {
		$menu_obj = get_post( $menu_item_id );

		if ( ! empty( $menu_obj->ID ) ) {
			$menu_obj        = wp_setup_nav_menu_item( $menu_obj );
			$menu_obj->title = empty( $menu_obj->title ) ? __( 'Menu Item' ) : $menu_obj->title;
			$menu_obj->label = $menu_obj->title; // Don't show "(pending)" in ajax-added items.
			$menu_items[]    = $menu_obj;
		}
	}

	/** This filter is documented in wp-admin/includes/nav-menu.php */
	$walker_class_name = apply_filters( 'wp_edit_nav_menu_walker', 'Walker_Nav_Menu_Edit', $_POST['menu'] );

	if ( ! class_exists( $walker_class_name ) ) {
		wp_die( 0 );
	}

	if ( ! empty( $menu_items ) ) {
		$args = array(
			'after'       => '',
			'before'      => '',
			'link_after'  => '',
			'link_before' => '',
			'walker'      => new $walker_class_name,
		);

		echo walk_nav_menu_tree( $menu_items, 0, (object) $args );
	}

	wp_die();
}