diff --git a/src/flask/app.py b/src/flask/app.py
index c6dd7833..cc326dbe 100644
--- a/src/flask/app.py
+++ b/src/flask/app.py
@@ -1318,8 +1318,8 @@ class Flask(App):
                 for func in reversed(self.after_request_funcs[name]):
                     response = self.ensure_sync(func)(response)
-        if not self.session_interface.is_null_session(ctx.session):
-            self.session_interface.save_session(self, ctx.session, response)
+        if not self.session_interface.is_null_session(ctx._session):
+            self.session_interface.save_session(self, ctx._session, response)
diff --git a/src/flask/ctx.py b/src/flask/ctx.py
index 222e818e..5f7b1f1d 100644
--- a/src/flask/ctx.py
+++ b/src/flask/ctx.py
@@ -324,7 +324,7 @@ class RequestContext:
-        self.session: SessionMixin | None = session
+        self._session: SessionMixin | None = session
@@ -351,7 +351,7 @@ class RequestContext:
             request=self.request,
-            session=self.session,
+            session=self._session,
         )
@@ -364,6 +364,16 @@ class RequestContext:
+    @property
+    def session(self) -> SessionMixin:
+        assert self._session is not None, "The session has not yet been opened."
+        self._session.accessed = True
+        return self._session
@@ -381,12 +391,12 @@ class RequestContext:
-        if self.session is None:
+        if self._session is None:
             session_interface = self.app.session_interface
-            self.session = session_interface.open_session(self.app, self.request)
+            self._session = session_interface.open_session(self.app, self.request)
-            if self.session is None:
-                self.session = session_interface.make_null_session(self.app)
+            if self._session is None:
+                self._session = session_interface.make_null_session(self.app)
diff --git a/src/flask/sessions.py b/src/flask/sessions.py
index 1841d882..ad357706 100644
--- a/src/flask/sessions.py
+++ b/src/flask/sessions.py
@@ -43,10 +43,15 @@ class SessionMixin(MutableMapping[str, t.Any]):
     #: ``True``.
     modified = True
-    accessed = True
+    accessed = False
@@ -65,34 +70,15 @@ class SecureCookieSession(CallbackDict[str, t.Any], SessionMixin):
     #: will only be written to the response if this is ``True``.
     modified = False
     def __init__(
         self,
-        initial: c.Mapping[str, t.Any] | c.Iterable[tuple[str, t.Any]] | None = None,
+        initial: c.Mapping[str, t.Any] | None = None,
     ) -> None:
         def on_update(self: te.Self) -> None:
             self.modified = True
-            self.accessed = True
         super().__init__(initial, on_update)
-    ...
 class NullSession(SecureCookieSession):
     """Class used to generate nicer error messages if sessions are not
diff --git a/src/flask/templating.py b/src/flask/templating.py
index 16d480f5..c5fb5b99 100644
--- a/src/flask/templating.py
+++ b/src/flask/templating.py
@@ -22,8 +22,8 @@ if t.TYPE_CHECKING:  # pragma: no cover
 def _default_template_ctx_processor() -> dict[str, t.Any]:
-    """Default template context processor.  Injects `request`,
-    `session` and `g`.
+    """Default template context processor.  Replaces the ``request`` and ``g``
+    proxies with their concrete objects for faster access.
     """
     appctx = _cv_app.get(None)
     reqctx = _cv_request.get(None)
@@ -32,7 +32,8 @@ def _default_template_ctx_processor() -> dict[str, t.Any]:
         rv["g"] = appctx.g
     if reqctx is not None:
         rv["request"] = reqctx.request
-        rv["session"] = reqctx.session
+        # The session proxy cannot be replaced, accessing it gets
+        # RequestContext.session, which sets session.accessed.
     return rv
diff --git a/tests/test_basic.py b/tests/test_basic.py
index c372a910..4b3374e2 100644
--- a/tests/test_basic.py
+++ b/tests/test_basic.py
@@ -231,27 +233,46 @@ def test_endpoint_decorator(app, client):
-def test_session(app, client):
+def test_session_accessed(app: flask.Flask, client: FlaskClient) -> None:
+    @app.post("/")
+    def do_set():
         flask.session["value"] = flask.request.form["value"]
         return "value set"
+    @app.get("/")
+    def do_get():
+        return flask.session.get("value", "None")
+    @app.get("/nothing")
+    def do_nothing() -> str:
+        return ""
+    with client:
+        rv = client.get("/nothing")
+        assert "cookie" not in rv.vary
+        assert not request_ctx._session.accessed
+    with client:
+        rv = client.post(data={"value": "42"})
+        assert "cookie" in rv.vary
+        assert request_ctx._session.accessed
+        assert request_ctx._session.modified
+    with client:
+        rv = client.get()
+        assert rv.text == "42"
+        assert "cookie" in rv.vary
+        assert request_ctx._session.accessed
+        assert not request_ctx._session.modified
+    with client:
+        rv = client.get("/nothing")
+        assert "cookie" not in rv.vary
+        assert not request_ctx._session.accessed