diff --git a/starlette/middleware/sessions.py b/starlette/middleware/sessions.py
index 3ff1e3de1..597de38a2 100644
--- a/starlette/middleware/sessions.py
+++ b/starlette/middleware/sessions.py
@@ -17,6 +17,7 @@ def __init__(
         secret_key: typing.Union[str, Secret],
         session_cookie: str = "session",
         max_age: typing.Optional[int] = 14 * 24 * 60 * 60,  # 14 days, in seconds
+        path: str = "/",
         same_site: str = "lax",
         https_only: bool = False,
     ) -> None:
@@ -24,6 +25,7 @@ def __init__(
         self.signer = itsdangerous.TimestampSigner(str(secret_key))
         self.session_cookie = session_cookie
         self.max_age = max_age
+        self.path = path
         self.security_flags = "httponly; samesite=" + same_site
         if https_only:  # Secure flag can be used with HTTPS only
             self.security_flags += "; secure"
@@ -49,7 +51,6 @@ async def __call__(self, scope: Scope, receive: Receive, send: Send) -> None:
 
         async def send_wrapper(message: Message) -> None:
             if message["type"] == "http.response.start":
-                path = scope.get("root_path", "") or "/"
                 if scope["session"]:
                     # We have session data to persist.
                     data = b64encode(json.dumps(scope["session"]).encode("utf-8"))
@@ -58,7 +59,7 @@ async def send_wrapper(message: Message) -> None:
                     header_value = "{session_cookie}={data}; path={path}; {max_age}{security_flags}".format(  # noqa E501
                         session_cookie=self.session_cookie,
                         data=data.decode("utf-8"),
-                        path=path,
+                        path=self.path,
                         max_age=f"Max-Age={self.max_age}; " if self.max_age else "",
                         security_flags=self.security_flags,
                     )
@@ -66,10 +67,12 @@ async def send_wrapper(message: Message) -> None:
                 elif not initial_session_was_empty:
                     # The session has been cleared.
                     headers = MutableHeaders(scope=message)
-                    header_value = "{}={}; {}".format(
-                        self.session_cookie,
-                        f"null; path={path}; expires=Thu, 01 Jan 1970 00:00:00 GMT;",
-                        self.security_flags,
+                    header_value = "{session_cookie}={data}; path={path}; {expires}{security_flags}".format(  # noqa E501
+                        session_cookie=self.session_cookie,
+                        data="null",
+                        path=self.path,
+                        expires="expires=Thu, 01 Jan 1970 00:00:00 GMT; ",
+                        security_flags=self.security_flags,
                     )
                     headers.append("Set-Cookie", header_value)
             await send(message)
diff --git a/tests/middleware/test_session.py b/tests/middleware/test_session.py
index 3cb755ed0..a044153a6 100644
--- a/tests/middleware/test_session.py
+++ b/tests/middleware/test_session.py
@@ -122,7 +122,9 @@ def test_session_cookie_subpath(test_client_factory):
         routes=[
             Route("/update_session", endpoint=update_session, methods=["POST"]),
         ],
-        middleware=[Middleware(SessionMiddleware, secret_key="example")],
+        middleware=[
+            Middleware(SessionMiddleware, secret_key="example", path="/second_app")
+        ],
     )
     app = Starlette(routes=[Mount("/second_app", app=second_app)])
     client = test_client_factory(app, base_url="http://testserver/second_app")