diff --git a/fastapi/security/open_id_connect_url.py b/fastapi/security/open_id_connect_url.py
index c8cceb911..c6b961ac0 100644
--- a/fastapi/security/open_id_connect_url.py
+++ b/fastapi/security/open_id_connect_url.py
@@ -1,11 +1,11 @@
-from typing import Optional
+from typing import Literal, Optional
 
 from fastapi.openapi.models import OpenIdConnect as OpenIdConnectModel
 from fastapi.security.base import SecurityBase
 from starlette.exceptions import HTTPException
 from starlette.requests import Request
-from starlette.status import HTTP_403_FORBIDDEN
-from typing_extensions import Annotated, Doc
+from starlette.status import HTTP_401_UNAUTHORIZED, HTTP_403_FORBIDDEN
+from typing_extensions import Annotated, Doc, deprecated
 
 
 class OpenIdConnect(SecurityBase):
@@ -65,20 +65,55 @@ class OpenIdConnect(SecurityBase):
                 """
             ),
         ] = True,
+        not_authenticated_status_code: Annotated[
+            Literal[401, 403],
+            Doc(
+                """
+                By default, if no HTTP Authorization header provided and `auto_error`
+                is set to `True`, it will automatically raise an`HTTPException` with
+                the status code `401`.
+
+                If your client relies on the old (incorrect) behavior and expects the
+                status code to be `403`, you can set `not_authenticated_status_code` to
+                `403` to achieve it.
+
+                Keep in mind that this parameter is temporary and will be removed in
+                the near future.
+                """
+            ),
+            deprecated(
+                """
+                This parameter is temporary. It was introduced to give users time
+                to upgrade their clients to follow the new behavior and will eventually
+                be removed.
+
+                Use it as a short-term workaround, but consider updating your clients
+                to align with the new behavior.
+                """
+            ),
+        ] = 401,
     ):
         self.model = OpenIdConnectModel(
             openIdConnectUrl=openIdConnectUrl, description=description
         )
         self.scheme_name = scheme_name or self.__class__.__name__
         self.auto_error = auto_error
+        self.not_authenticated_status_code = not_authenticated_status_code
 
     async def __call__(self, request: Request) -> Optional[str]:
         authorization = request.headers.get("Authorization")
         if not authorization:
             if self.auto_error:
-                raise HTTPException(
-                    status_code=HTTP_403_FORBIDDEN, detail="Not authenticated"
-                )
+                if self.not_authenticated_status_code == HTTP_403_FORBIDDEN:
+                    raise HTTPException(
+                        status_code=HTTP_403_FORBIDDEN, detail="Not authenticated"
+                    )
+                else:
+                    raise HTTPException(
+                        status_code=HTTP_401_UNAUTHORIZED,
+                        detail="Not authenticated",
+                        headers={"WWW-Authenticate": "Bearer"},
+                    )
             else:
                 return None
         return authorization
diff --git a/tests/test_security_openid_connect.py b/tests/test_security_openid_connect.py
index 1e322e640..c9a0a8db7 100644
--- a/tests/test_security_openid_connect.py
+++ b/tests/test_security_openid_connect.py
@@ -39,8 +39,9 @@ def test_security_oauth2_password_other_header():
 
 def test_security_oauth2_password_bearer_no_header():
     response = client.get("/users/me")
-    assert response.status_code == 403, response.text
+    assert response.status_code == 401, response.text
     assert response.json() == {"detail": "Not authenticated"}
+    assert response.headers["WWW-Authenticate"] == "Bearer"
 
 
 def test_openapi_schema():
diff --git a/tests/test_security_openid_connect_description.py b/tests/test_security_openid_connect_description.py
index 44cf57f86..d008cbc63 100644
--- a/tests/test_security_openid_connect_description.py
+++ b/tests/test_security_openid_connect_description.py
@@ -41,8 +41,9 @@ def test_security_oauth2_password_other_header():
 
 def test_security_oauth2_password_bearer_no_header():
     response = client.get("/users/me")
-    assert response.status_code == 403, response.text
+    assert response.status_code == 401, response.text
     assert response.json() == {"detail": "Not authenticated"}
+    assert response.headers["WWW-Authenticate"] == "Bearer"
 
 
 def test_openapi_schema():
diff --git a/tests/test_security_status_code_403_option.py b/tests/test_security_status_code_403_option.py
index bf91f6202..29866bfd4 100644
--- a/tests/test_security_status_code_403_option.py
+++ b/tests/test_security_status_code_403_option.py
@@ -1,7 +1,10 @@
+from typing import Union
+
 import pytest
 from fastapi import FastAPI, Security
 from fastapi.security.api_key import APIKeyBase, APIKeyCookie, APIKeyHeader, APIKeyQuery
 from fastapi.security.http import HTTPBase, HTTPBearer, HTTPDigest
+from fastapi.security.open_id_connect_url import OpenIdConnect
 from fastapi.testclient import TestClient
 
 
@@ -61,9 +64,10 @@ def test_apikey_status_code_403_on_auth_error_no_auto_error(auth: APIKeyBase):
     "auth",
     [
         HTTPBearer(not_authenticated_status_code=403),
+        OpenIdConnect(not_authenticated_status_code=403, openIdConnectUrl="/openid"),
     ],
 )
-def test_oauth2_status_code_403_on_auth_error(auth: HTTPBase):
+def test_oauth2_status_code_403_on_auth_error(auth: Union[HTTPBase, OpenIdConnect]):
     """
     Test temporary `not_authenticated_status_code` parameter for security classes that
     follow rfc6750.
@@ -86,10 +90,15 @@ def test_oauth2_status_code_403_on_auth_error(auth: HTTPBase):
     "auth",
     [
         HTTPBearer(not_authenticated_status_code=403, auto_error=False),
+        OpenIdConnect(
+            not_authenticated_status_code=403,
+            openIdConnectUrl="/openid",
+            auto_error=False,
+        ),
     ],
 )
 def test_oauth2_status_code_403_on_auth_error_no_auto_error(
-    auth: HTTPBase,
+    auth: Union[HTTPBase, OpenIdConnect],
 ):
     """
     Test temporary `not_authenticated_status_code` parameter for security classes that