diff --git a/src/wp-includes/rest-api/endpoints/class-wp-rest-posts-controller.php b/src/wp-includes/rest-api/endpoints/class-wp-rest-posts-controller.php
index 018b66e..e791cd6 100644
--- a/src/wp-includes/rest-api/endpoints/class-wp-rest-posts-controller.php
+++ b/src/wp-includes/rest-api/endpoints/class-wp-rest-posts-controller.php
@@ -574,7 +574,7 @@ class WP_REST_Posts_Controller extends WP_REST_Controller {
 		}
 
 		if ( ! empty( $schema['properties']['template'] ) && isset( $request['template'] ) ) {
-			$this->handle_template( $request['template'], $post_id );
+			$this->handle_template( $request['template'], $post_id, true );
 		}
 
 		$terms_update = $this->handle_terms( $post_id, $request );
@@ -1070,6 +1070,11 @@ class WP_REST_Posts_Controller extends WP_REST_Controller {
 			$prepared_post->ping_status = $request['ping_status'];
 		}
 
+		if ( ! empty( $schema['properties']['template'] ) ) {
+			// Force template to null so that it can be handled exclusively by the REST controller.
+			$prepared_post->page_template = null;
+		}
+
 		/**
 		 * Filters a post before it is inserted via the REST API.
 		 *
@@ -1147,19 +1152,60 @@ class WP_REST_Posts_Controller extends WP_REST_Controller {
 	}
 
 	/**
+	 * Check whether the template is valid for the given post.
+	 *
+	 * @since 4.9.0
+	 *
+	 * @param string          $template
+	 * @param WP_REST_Request $request
+	 *
+	 * @return bool|WP_Error True if template is still valid or if the same as existing value, or false if template not supported.
+	 */
+	public function check_template( $template, $request ) {
+
+		if ( ! $template ) {
+			return true;
+		}
+
+		if ( $request['id'] ) {
+			$current_template = get_page_template_slug( $request['id'] );
+		} else {
+			$current_template = '';
+		}
+
+		// Always allow for updating a post to the same template, even if that template is no longer supported.
+		if ( $template === $current_template ) {
+			return true;
+		}
+
+		// If this is a create request, get_post() will return null and wp theme will fallback to the passed post type.
+		$allowed_templates = wp_get_theme()->get_page_templates( get_post( $request['id'] ), $this->post_type );
+
+		if ( isset( $allowed_templates[ $template ] ) ) {
+			return true;
+		}
+
+		/* translators: 1: parameter, 2: list of valid values */
+		return new WP_Error( 'rest_invalid_param', sprintf( __( '%1$s is not one of %2$s.' ), 'template', implode( ', ', array_keys( $allowed_templates ) ) ) );
+	}
+
+	/**
 	 * Sets the template for a post.
 	 *
 	 * @since 4.7.0
+	 * @since 4.9.0 Introduced the $validate parameter.
 	 *
 	 * @param string  $template Page template filename.
 	 * @param integer $post_id  Post ID.
+	 * @param bool    $validate Whether to validate that the template selected is valid.
 	 */
-	public function handle_template( $template, $post_id ) {
-		if ( in_array( $template, array_keys( wp_get_theme()->get_page_templates( get_post( $post_id ) ) ), true ) ) {
-			update_post_meta( $post_id, '_wp_page_template', $template );
-		} else {
-			update_post_meta( $post_id, '_wp_page_template', '' );
+	public function handle_template( $template, $post_id, $validate = false ) {
+
+		if ( $validate && ! array_key_exists( $template, wp_get_theme()->get_page_templates( get_post( $post_id ) ) ) ) {
+			$template = '';
 		}
+
+		update_post_meta( $post_id, '_wp_page_template', $template );
 	}
 
 	/**
@@ -1994,6 +2040,9 @@ class WP_REST_Posts_Controller extends WP_REST_Controller {
 			'type'        => 'string',
 			'enum'        => array_merge( array_keys( wp_get_theme()->get_page_templates( null, $this->post_type ) ), array( '' ) ),
 			'context'     => array( 'view', 'edit' ),
+			'arg_options' => array(
+				'validate_callback' => array( $this, 'check_template' ),
+			),
 		);
 
 		$taxonomies = wp_list_filter( get_object_taxonomies( $this->post_type, 'objects' ), array( 'show_in_rest' => true ) );
diff --git a/tests/phpunit/tests/rest-api/rest-posts-controller.php b/tests/phpunit/tests/rest-api/rest-posts-controller.php
index c86879c..b769003 100644
--- a/tests/phpunit/tests/rest-api/rest-posts-controller.php
+++ b/tests/phpunit/tests/rest-api/rest-posts-controller.php
@@ -2649,6 +2649,30 @@ class WP_Test_REST_Posts_Controller extends WP_Test_REST_Post_Type_Controller_Te
 		$this->assertEquals( '', $post_template );
 	}
 
+	/**
+	 * @ticket 39996
+	 */
+	public function test_update_item_with_same_template_that_no_longer_exists() {
+
+		wp_set_current_user( self::$editor_id );
+
+		update_post_meta( self::$post_id, '_wp_page_template', 'post-my-invalid-template.php' );
+
+		$request = new WP_REST_Request( 'PUT', sprintf( '/wp/v2/posts/%d', self::$post_id ) );
+		$params = $this->set_post_data( array(
+			'template' => 'post-my-invalid-template.php',
+		) );
+		$request->set_body_params( $params );
+		$response = $this->server->dispatch( $request );
+
+		$this->assertEquals( 200, $response->get_status() );
+
+		$data = $response->get_data();
+		$post_template = get_page_template_slug( get_post( $data['id'] ) );
+
+		$this->assertEquals( 'post-my-invalid-template.php', $post_template );
+		$this->assertEquals( 'post-my-invalid-template.php', $data['template'] );
+	}
 
 	public function verify_post_roundtrip( $input = array(), $expected_output = array() ) {
 		// Create the post