diff --git a/src/wp-includes/class-wp-script-modules.php b/src/wp-includes/class-wp-script-modules.php
index 22c4e29a286c8..4c542211b86bf 100644
--- a/src/wp-includes/class-wp-script-modules.php
+++ b/src/wp-includes/class-wp-script-modules.php
@@ -100,13 +100,46 @@ public function register( $module_id, $src, $deps = array(), $version = false )
 	 * Marks the module to be enqueued in the page the next time
 	 * `prints_enqueued_modules` is called.
 	 *
+	 * If a src is provided and the module has not been registered yet, it will be
+	 * registered.
+	 *
 	 * @since 6.5.0
 	 *
-	 * @param string $module_id The identifier of the module.
+	 * @param string                                                        $module_id The identifier of the module.
+	 *                                                                                 Should be unique. It will be used
+	 *                                                                                 in the final import map.
+	 * @param string                                                        $src       Optional. Full URL of the module,
+	 *                                                                                 or path of the module relative to
+	 *                                                                                 the WordPress root directory. If
+	 *                                                                                 it is provided and the module has
+	 *                                                                                 not been registered yet, it will be
+	 *                                                                                 registered.
+	 * @param array<string|array{id: string, import?: 'static'|'dynamic' }> $deps      Optional. An array of module
+	 *                                                                                 identifiers of the dependencies of
+	 *                                                                                 this module. The dependencies can
+	 *                                                                                 be strings or arrays. If they are
+	 *                                                                                 arrays, they need an `id` key with
+	 *                                                                                 the module identifier, and can
+	 *                                                                                 contain an `import` key with either
+	 *                                                                                 `static` or `dynamic`. By default,
+	 *                                                                                 dependencies that don't contain an
+	 *                                                                                 `import` key are considered static.
+	 * @param string|false|null                                             $version   Optional. String specifying the
+	 *                                                                                 module version number. Defaults to
+	 *                                                                                 false. It is added to the URL as a
+	 *                                                                                 query string for cache busting
+	 *                                                                                 purposes. If $version is set to
+	 *                                                                                 false, the version number is the
+	 *                                                                                 currently installed WordPress
+	 *                                                                                 version. If $version is set to
+	 *                                                                                 null, no version is added.
 	 */
-	public function enqueue( $module_id ) {
+	public function enqueue( $module_id, $src = '', $deps = array(), $version = false ) {
 		if ( isset( $this->registered[ $module_id ] ) ) {
 			$this->registered[ $module_id ]['enqueue'] = true;
+		} elseif ( $src ) {
+			$this->register( $module_id, $src, $deps, $version );
+			$this->registered[ $module_id ]['enqueue'] = true;
 		} else {
 			$this->enqueued_before_registered[ $module_id ] = true;
 		}
diff --git a/src/wp-includes/script-modules.php b/src/wp-includes/script-modules.php
index b3ef52870d489..52552317e4aa5 100644
--- a/src/wp-includes/script-modules.php
+++ b/src/wp-includes/script-modules.php
@@ -66,12 +66,42 @@ function wp_register_module( $module_id, $src, $deps = array(), $version = false
 /**
  * Marks the module to be enqueued in the page.
  *
+ * If a src is provided and the module has not been registered yet, it will be
+ * registered.
+ *
  * @since 6.5.0
  *
- * @param string $module_id The identifier of the module.
+ * @param string                                                        $module_id The identifier of the module.
+ *                                                                                 Should be unique. It will be used
+ *                                                                                 in the final import map.
+ * @param string                                                        $src       Optional. Full URL of the module,
+ *                                                                                 or path of the module relative to
+ *                                                                                 the WordPress root directory. If
+ *                                                                                 it is provided and the module has
+ *                                                                                 not been registered yet, it will be
+ *                                                                                 registered.
+ * @param array<string|array{id: string, import?: 'static'|'dynamic' }> $deps      Optional. An array of module
+ *                                                                                 identifiers of the dependencies of
+ *                                                                                 this module. The dependencies can
+ *                                                                                 be strings or arrays. If they are
+ *                                                                                 arrays, they need an `id` key with
+ *                                                                                 the module identifier, and can
+ *                                                                                 contain an `import` key with either
+ *                                                                                 `static` or `dynamic`. By default,
+ *                                                                                 dependencies that don't contain an
+ *                                                                                 `import` key are considered static.
+ * @param string|false|null                                             $version   Optional. String specifying the
+ *                                                                                 module version number. Defaults to
+ *                                                                                 false. It is added to the URL as a
+ *                                                                                 query string for cache busting
+ *                                                                                 purposes. If $version is set to
+ *                                                                                 false, the version number is the
+ *                                                                                 currently installed WordPress
+ *                                                                                 version. If $version is set to
+ *                                                                                 null, no version is added.
  */
-function wp_enqueue_module( $module_id ) {
-	wp_modules()->enqueue( $module_id );
+function wp_enqueue_module( $module_id, $src = '', $deps = array(), $version = false ) {
+	wp_modules()->enqueue( $module_id, $src, $deps, $version );
 }
 
 /**
diff --git a/tests/phpunit/tests/script-modules/wpScriptModules.php b/tests/phpunit/tests/script-modules/wpScriptModules.php
index e8947cb14e92b..2c82b592caacf 100644
--- a/tests/phpunit/tests/script-modules/wpScriptModules.php
+++ b/tests/phpunit/tests/script-modules/wpScriptModules.php
@@ -583,4 +583,87 @@ public function test_print_preloaded_modules_can_be_called_multiple_times() {
 		$preloaded_modules = $this->get_preloaded_modules();
 		$this->assertCount( 0, $preloaded_modules );
 	}
+
+	/**
+	 * Tests that a module is not registered when calling enqueue without a valid
+	 * src.
+	 *
+	 * @ticket 56313
+	 *
+	 * @covers ::enqueue()
+	 * @covers ::print_enqueued_modules()
+	 */
+	public function test_wp_enqueue_module_doesnt_register_without_a_valid_src() {
+		$this->modules->enqueue( 'foo' );
+
+		$enqueued_modules = $this->get_enqueued_modules();
+
+		$this->assertCount( 0, $enqueued_modules );
+		$this->assertFalse( isset( $enqueued_modules['foo'] ) );
+	}
+
+	/**
+	 * Tests that a module is registered when calling enqueue with a valid src.
+	 *
+	 * @ticket 56313
+	 *
+	 * @covers ::enqueue()
+	 * @covers ::print_enqueued_modules()
+	 */
+	public function test_wp_enqueue_module_registers_with_valid_src() {
+		$this->modules->enqueue( 'foo', '/foo.js' );
+
+		$enqueued_modules = $this->get_enqueued_modules();
+
+		$this->assertCount( 1, $enqueued_modules );
+		$this->assertStringStartsWith( '/foo.js', $enqueued_modules['foo'] );
+	}
+
+	/**
+	 * Tests that a module is registered when calling enqueue with a valid src the
+	 * second time.
+	 *
+	 * @ticket 56313
+	 *
+	 * @covers ::enqueue()
+	 * @covers ::print_enqueued_modules()
+	 */
+	public function test_wp_enqueue_module_registers_with_valid_src_the_second_time() {
+		$this->modules->enqueue( 'foo' ); // Not valid src.
+
+		$enqueued_modules = $this->get_enqueued_modules();
+
+		$this->assertCount( 0, $enqueued_modules );
+		$this->assertFalse( isset( $enqueued_modules['foo'] ) );
+
+		$this->modules->enqueue( 'foo', '/foo.js' ); // Valid src.
+
+		$enqueued_modules = $this->get_enqueued_modules();
+
+		$this->assertCount( 1, $enqueued_modules );
+		$this->assertStringStartsWith( '/foo.js', $enqueued_modules['foo'] );
+	}
+
+	/**
+	 * Tests that a module is registered with all the params when calling enqueue.
+	 *
+	 * @ticket 56313
+	 *
+	 * @covers ::register()
+	 * @covers ::enqueue()
+	 * @covers ::print_enqueued_modules()
+	 * @covers ::print_import_map()
+	 */
+	public function test_wp_enqueue_module_registers_all_params() {
+		$this->modules->enqueue( 'foo', '/foo.js', array( 'dep' ), '1.0' );
+		$this->modules->register( 'dep', '/dep.js' );
+
+		$enqueued_modules = $this->get_enqueued_modules();
+		$import_map       = $this->get_import_map();
+
+		$this->assertCount( 1, $enqueued_modules );
+		$this->assertEquals( '/foo.js?ver=1.0', $enqueued_modules['foo'] );
+		$this->assertCount( 1, $import_map );
+		$this->assertStringStartsWith( '/dep.js', $import_map['dep'] );
+	}
 }