diff --git a/assets/js/app.js b/assets/js/app.js
index f2ff42d11..b01999ae7 100644
--- a/assets/js/app.js
+++ b/assets/js/app.js
@@ -62,44 +62,65 @@ function connect() {
 }
 
 // When Livebook runs in a cross-origin iframe the browser may restrict access
-// to cookies. This is the case in Safari with the "Prevent cross-site tracking"
-// option enabled, which is the default. Without cookies access, the session
-// is not stored, so CSRF tokens are invalid. Consequently, LV keeps reloading
-// the page, as we try to connect the socket with invalid token. To work around
-// this we tell the user to open Livebook outside the iframe.
+// to cookies. Without cookies access, the session is not stored, so CSRF tokens
+// are invalid. Consequently, LV keeps reloading the page, as we try to connect
+// the socket with invalid token. To work around this we tell the user to open
+// Livebook outside the iframe.
+//
+// The behaviour varies across browsers and browsing modes (regular and private).
+// A few examples (at the time of writing):
+//
+//   * Safari by default blocks all cross-origin cookies. This is controlled by
+//     the "Prevent cross-site tracking" option
+//
+//   * Chrome in incognito mode blocks all cross-origin cookies, can be relaxed
+//     on per-site basis
+//
+//   * Firefox implements state partitioning (1) and it is enabled for storage
+//     by default since Firefox 103 (2). With storage partitioning, the embedded
+//     site gets a separate storage bucket scoped by the top-level origin, so
+//     the site generally works as expected
+//
+//   * Brave also implements storage partitioning (3)
+//
+// To detect whether cookies are allowed, we check for the user data cookie,
+// which should be set by the server on the initial request and is accessible
+// from JavaScript (without HttpOnly).
+//
+// Also see the proposal (4), which may streamline this in the future.
+//
+// (1): https://developer.mozilla.org/en-US/docs/Web/Privacy/State_Partitioning#state_partitioning
+// (2): https://www.mozilla.org/en-US/firefox/103.0/releasenotes
+// (3): https://brave.com/privacy-updates/7-ephemeral-storage
+// (4): https://github.com/privacycg/CHIPS
 
-if (document.hasStorageAccess) {
-  document.hasStorageAccess().then((hasStorageAccess) => {
-    if (hasStorageAccess) {
-      connect();
-    } else {
-      const overlayEl = document.createElement("div");
+if (loadUserData() === null) {
+  const overlayEl = document.createElement("div");
 
-      overlayEl.innerHTML = `
-        <div class="fixed top-0 bottom-0 left-0 right-0 z-[1000] px-4 py-8 bg-gray-900/95 flex justify-center items-center">
-          <div class="max-w-[600px] w-full flex flex-col">
-            <div class="text-xl text-gray-100 font-medium">
-              Action required
-            </div>
-            <div class="mt-3 text-sm text-gray-300">
-              It looks like Livebook does not have access to cookies. This usually happens when
-              it runs in an iframe. To make sure the app is fully functional open it in a new
-              tab directly.
-            </div>
-            <div class="mt-6">
-              <a id="open-app" class="button-base button-blue" target="_blank">
-                Open app
-              </a>
-            </div>
-          </div>
+  overlayEl.innerHTML = `
+    <div class="fixed top-0 bottom-0 left-0 right-0 z-[1000] px-4 py-8 bg-gray-900/95 flex justify-center items-center">
+      <div class="max-w-[600px] w-full flex flex-col">
+        <div class="text-xl text-gray-100 font-medium">
+          Action required
         </div>
-      `;
+        <div class="mt-3 text-sm text-gray-300">
+          It looks like Livebook does not have access to cookies. This usually happens when
+          it runs in an iframe. To make sure the app is fully functional open it in a new
+          tab directly. Alternatively you can relax security settings for this page to allow
+          third-party cookies.
+        </div>
+        <div class="mt-6">
+          <a id="open-app" class="button-base button-blue" target="_blank">
+            Open app
+          </a>
+        </div>
+      </div>
+    </div>
+  `;
 
-      overlayEl.querySelector("#open-app").href = window.location;
+  overlayEl.querySelector("#open-app").href = window.location;
 
-      document.body.appendChild(overlayEl);
-    }
-  });
+  document.body.appendChild(overlayEl);
 } else {
   connect();
 }
diff --git a/assets/js/lib/user.js b/assets/js/lib/user.js
index a9de85826..7929a2b82 100644
--- a/assets/js/lib/user.js
+++ b/assets/js/lib/user.js
@@ -38,6 +38,14 @@ function getCookieValue(key) {
 }
 
 function setCookie(key, value, maxAge) {
-  const cookie = `${key}=${value};max-age=${maxAge};path=/`;
+  const cookie = `${key}=${value};max-age=${maxAge};path=/${cookieOptions()}`;
   document.cookie = cookie;
 }
+
+function cookieOptions() {
+  if (document.body.hasAttribute("data-within-iframe")) {
+    return ";SameSite=None;Secure";
+  } else {
+    return ";SameSite=Lax";
+  }
+}
diff --git a/lib/livebook_web/components/layouts/root.html.heex b/lib/livebook_web/components/layouts/root.html.heex
index 01625384c..a44002000 100644
--- a/lib/livebook_web/components/layouts/root.html.heex
+++ b/lib/livebook_web/components/layouts/root.html.heex
@@ -20,6 +20,7 @@
   <body
     class="bg-white"
     data-feature-flags={Livebook.Config.enabled_feature_flags() |> Enum.join(",")}
+    data-within-iframe={Livebook.Config.within_iframe?()}
   >
     <%= @inner_content %>
   </body>
diff --git a/lib/livebook_web/plugs/user_plug.ex b/lib/livebook_web/plugs/user_plug.ex
index 1b51d4078..c764dcd34 100644
--- a/lib/livebook_web/plugs/user_plug.ex
+++ b/lib/livebook_web/plugs/user_plug.ex
@@ -45,9 +45,23 @@ defmodule LivebookWeb.UserPlug do
     else
       user_data = user_data(User.new())
       encoded = user_data |> Jason.encode!() |> Base.encode64()
-      # Set `http_only` to `false`, so that it can be accessed on the client
-      # Set expiration in 5 years
-      put_resp_cookie(conn, "lb:user_data", encoded, http_only: false, max_age: 157_680_000)
+
+      put_resp_cookie(
+        conn,
+        "lb:user_data",
+        encoded,
+        # We disable HttpOnly, so that it can be accessed on the client
+        # and set expiration to 5 years
+        [http_only: false, max_age: 157_680_000] ++ cookie_options()
+      )
+    end
+  end
+
+  defp cookie_options() do
+    if Livebook.Config.within_iframe?() do
+      [same_site: "None", secure: true]
+    else
+      [same_site: "Lax"]
     end
   end