diff --git a/fastapi/security/http.py b/fastapi/security/http.py
index 16abf9b65..f332bcf0f 100644
--- a/fastapi/security/http.py
+++ b/fastapi/security/http.py
@@ -74,10 +74,13 @@ class HTTPBase(SecurityBase):
         scheme_name: Optional[str] = None,
         description: Optional[str] = None,
         auto_error: bool = True,
+        not_authenticated_status_code: Literal[401, 403] = 401,
     ):
         self.model = HTTPBaseModel(scheme=scheme, description=description)
+        self.model_scheme = scheme
         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
@@ -86,9 +89,16 @@ class HTTPBase(SecurityBase):
         scheme, credentials = get_authorization_scheme_param(authorization)
         if not (authorization and scheme and credentials):
             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": self.model_scheme},
+                    )
             else:
                 return None
         return HTTPAuthorizationCredentials(scheme=scheme, credentials=credentials)
diff --git a/tests/test_security_http_base.py b/tests/test_security_http_base.py
index 51928bafd..8cf259a75 100644
--- a/tests/test_security_http_base.py
+++ b/tests/test_security_http_base.py
@@ -23,8 +23,9 @@ def test_security_http_base():
 
 def test_security_http_base_no_credentials():
     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"] == "Other"
 
 
 def test_openapi_schema():
diff --git a/tests/test_security_http_base_description.py b/tests/test_security_http_base_description.py
index bc79f3242..791ea59f4 100644
--- a/tests/test_security_http_base_description.py
+++ b/tests/test_security_http_base_description.py
@@ -23,8 +23,9 @@ def test_security_http_base():
 
 def test_security_http_base_no_credentials():
     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"] == "Other"
 
 
 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 084236298..bf91f6202 100644
--- a/tests/test_security_status_code_403_option.py
+++ b/tests/test_security_status_code_403_option.py
@@ -147,3 +147,43 @@ def test_digest_status_code_403_on_auth_error_no_auto_error():
 
     response = client.get("/")
     assert response.status_code == 200
+
+
+def test_httpbase_status_code_403_on_auth_error():
+    """
+    Test temporary `not_authenticated_status_code` parameter for `HTTPBase` class.
+    """
+
+    app = FastAPI()
+
+    auth = HTTPBase(scheme="Other", not_authenticated_status_code=403)
+
+    @app.get("/")
+    async def protected(_: str = Security(auth)):
+        pass  # pragma: no cover
+
+    client = TestClient(app)
+
+    response = client.get("/")
+    assert response.status_code == 403
+    assert response.json() == {"detail": "Not authenticated"}
+
+
+def test_httpbase_status_code_403_on_auth_error_no_auto_error():
+    """
+    Test temporary `not_authenticated_status_code` parameter for `HTTPBase` class with
+    `auto_error=False`.
+    """
+
+    app = FastAPI()
+
+    auth = HTTPBase(scheme="Other", not_authenticated_status_code=403, auto_error=False)
+
+    @app.get("/")
+    async def protected(_: str = Security(auth)):
+        pass  # pragma: no cover
+
+    client = TestClient(app)
+
+    response = client.get("/")
+    assert response.status_code == 200