diff --git a/packages/playwright-core/src/server/webkit/wkBrowser.ts b/packages/playwright-core/src/server/webkit/wkBrowser.ts
index 4b10dfd3fea5c..2ce858a183684 100644
--- a/packages/playwright-core/src/server/webkit/wkBrowser.ts
+++ b/packages/playwright-core/src/server/webkit/wkBrowser.ts
@@ -267,7 +267,8 @@ export class WKBrowserContext extends BrowserContext {
     const cc = network.rewriteCookies(cookies).map(c => ({
       ...c,
       session: c.expires === -1 || c.expires === undefined,
-      expires: c.expires && c.expires !== -1 ? c.expires * 1000 : c.expires
+      expires: c.expires && c.expires !== -1 ? c.expires * 1000 : c.expires,
+      sameSite: c.sameSite ? c.sameSite : 'Lax',
     })) as Protocol.Playwright.SetCookieParam[];
     await this._browser._browserSession.send('Playwright.setCookies', { cookies: cc, browserContextId: this._browserContextId });
   }
diff --git a/tests/config/browserTest.ts b/tests/config/browserTest.ts
index 02555d42eb412..44f4a9f39acad 100644
--- a/tests/config/browserTest.ts
+++ b/tests/config/browserTest.ts
@@ -67,9 +67,11 @@ const test = baseTest.extend<BrowserTestTestFixtures, BrowserTestWorkerFixtures>
       await run(false);
   }, { scope: 'worker' }],
 
-  defaultSameSiteCookieValue: [async ({ browserName, browserMajorVersion, channel }, run) => {
+  defaultSameSiteCookieValue: [async ({ browserName, browserMajorVersion, channel, platform }, run) => {
     if (browserName === 'chromium')
       await run('Lax');
+    else if (browserName === 'webkit' && platform === 'linux')
+      await run('Lax');
     else if (browserName === 'webkit')
       await run('None');
     else if (browserName === 'firefox' && channel === 'firefox-beta')
diff --git a/tests/library/browsercontext-add-cookies.spec.ts b/tests/library/browsercontext-add-cookies.spec.ts
index bdfe14ef0a17e..b6cd243c79d9a 100644
--- a/tests/library/browsercontext-add-cookies.spec.ts
+++ b/tests/library/browsercontext-add-cookies.spec.ts
@@ -224,7 +224,7 @@ it('should have |expires| set to |-1| for session cookies', async ({ context, se
   expect(cookies[0].expires).toBe(-1);
 });
 
-it('should set cookie with reasonable defaults', async ({ context, server, browserName }) => {
+it('should set cookie with reasonable defaults', async ({ context, server, browserName, defaultSameSiteCookieValue }) => {
   await context.addCookies([{
     url: server.EMPTY_PAGE,
     name: 'defaults',
@@ -239,7 +239,7 @@ it('should set cookie with reasonable defaults', async ({ context, server, brows
     expires: -1,
     httpOnly: false,
     secure: false,
-    sameSite: browserName === 'chromium' ? 'Lax' : 'None',
+    sameSite: defaultSameSiteCookieValue,
   }]);
 });
 
diff --git a/tests/library/browsercontext-cookies.spec.ts b/tests/library/browsercontext-cookies.spec.ts
index a53f989886c64..e64381e3d6006 100644
--- a/tests/library/browsercontext-cookies.spec.ts
+++ b/tests/library/browsercontext-cookies.spec.ts
@@ -350,26 +350,26 @@ it('should be able to send third party cookies via an iframe', async ({ browser,
   }
 });
 
-it('should support requestStorageAccess', async ({ page, server, channel, browserName, isMac, isLinux, isWindows }) => {
+it('should support requestStorageAccess', async ({ browser, httpsServer, channel, browserName, isLinux, isMac }) => {
+  const page = await browser.newPage({ ignoreHTTPSErrors: true });
   it.info().annotations.push({ type: 'issue', description: 'https://github.com/microsoft/playwright/issues/17285' });
   it.skip(browserName === 'chromium', 'requestStorageAccess API is not available in Chromium');
   it.skip(channel === 'firefox-beta', 'hasStorageAccess returns true, but no cookie is sent');
-
-  server.setRoute('/set-cookie.html', (req, res) => {
-    res.setHeader('Set-Cookie', 'name=value; Path=/');
+  httpsServer.setRoute('/set-cookie.html', (req, res) => {
+    res.setHeader('Set-Cookie', 'name=value; Path=/; SameSite=None; Secure');
     res.end();
   });
   // Navigate once to the domain as top level.
-  await page.goto(server.CROSS_PROCESS_PREFIX + '/set-cookie.html');
-  await page.goto(server.EMPTY_PAGE);
-  await page.setContent(`<iframe src="${server.CROSS_PROCESS_PREFIX + '/empty.html'}"></iframe>`);
+  await page.goto(httpsServer.CROSS_PROCESS_PREFIX + '/set-cookie.html');
+  await page.goto(httpsServer.EMPTY_PAGE);
+  await page.setContent(`<iframe src="${httpsServer.CROSS_PROCESS_PREFIX + '/empty.html'}"></iframe>`);
 
   const frame = page.frames()[1];
   if (browserName === 'firefox') {
     expect(await frame.evaluate(() => document.hasStorageAccess())).toBeTruthy();
     {
       const [serverRequest] = await Promise.all([
-        server.waitForRequest('/title.html'),
+        httpsServer.waitForRequest('/title.html'),
         frame.evaluate(() => fetch('/title.html'))
       ]);
       expect(serverRequest.headers.cookie).toBe('name=value');
@@ -381,7 +381,7 @@ it('should support requestStorageAccess', async ({ page, server, channel, browse
       expect(await frame.evaluate(() => document.hasStorageAccess())).toBeFalsy();
     {
       const [serverRequest] = await Promise.all([
-        server.waitForRequest('/title.html'),
+        httpsServer.waitForRequest('/title.html'),
         frame.evaluate(() => fetch('/title.html'))
       ]);
       if (!isMac && browserName === 'webkit')
@@ -393,12 +393,13 @@ it('should support requestStorageAccess', async ({ page, server, channel, browse
     expect(await frame.evaluate(() => document.hasStorageAccess())).toBeTruthy();
     {
       const [serverRequest] = await Promise.all([
-        server.waitForRequest('/title.html'),
+        httpsServer.waitForRequest('/title.html'),
         frame.evaluate(() => fetch('/title.html'))
       ]);
       expect(serverRequest.headers.cookie).toBe('name=value');
     }
   }
+  await page.close();
 });
 
 it('should parse cookie with large Max-Age correctly', async ({ server, page, defaultSameSiteCookieValue, browserName, platform }) => {
diff --git a/tests/library/browsercontext-fetch.spec.ts b/tests/library/browsercontext-fetch.spec.ts
index bb0bb15362922..a82704d8fec17 100644
--- a/tests/library/browsercontext-fetch.spec.ts
+++ b/tests/library/browsercontext-fetch.spec.ts
@@ -1155,7 +1155,7 @@ it('should support set-cookie with SameSite and without Secure attribute over HT
       });
       await page.request.get(server.EMPTY_PAGE);
       const [cookie] = await page.context().cookies();
-      if (browserName === 'chromium' && value === 'None')
+      if (['chromium', 'webkit'].includes(browserName) && value === 'None')
         expect(cookie).toBeFalsy();
       else if (browserName === 'webkit' && isWindows)
         expect(cookie.sameSite).toBe('None');