diff --git a/moto/cognitoidp/models.py b/moto/cognitoidp/models.py
index e8857f510..3ddb8f113 100644
--- a/moto/cognitoidp/models.py
+++ b/moto/cognitoidp/models.py
@@ -1429,7 +1429,7 @@ class CognitoIdpBackend(BaseBackend):
                 }
 
             return self._log_user_in(user_pool, client, username)
-        elif auth_flow is AuthFlow.REFRESH_TOKEN:
+        elif auth_flow in (AuthFlow.REFRESH_TOKEN, AuthFlow.REFRESH_TOKEN_AUTH):
             refresh_token: str = auth_parameters.get("REFRESH_TOKEN")  # type: ignore[assignment]
             (
                 access_token,