diff --git a/packages/playwright-core/src/server/socksClientCertificatesInterceptor.ts b/packages/playwright-core/src/server/socksClientCertificatesInterceptor.ts
index 08aaa4f25a137..b041ffb8290e2 100644
--- a/packages/playwright-core/src/server/socksClientCertificatesInterceptor.ts
+++ b/packages/playwright-core/src/server/socksClientCertificatesInterceptor.ts
@@ -346,7 +346,7 @@ function rewriteToLocalhostIfNeeded(host: string): string {
 }
 
 export function rewriteOpenSSLErrorIfNeeded(error: Error): Error {
-  if (error.message !== 'unsupported')
+  if (error.message !== 'unsupported' && (error as NodeJS.ErrnoException).code !== 'ERR_CRYPTO_UNSUPPORTED_OPERATION')
     return error;
   return rewriteErrorMessage(error, [
     'Unsupported TLS certificate.',
diff --git a/tests/playwright-test/babel.spec.ts b/tests/playwright-test/babel.spec.ts
index 3fb0a1a725762..724a2a98ad04c 100644
--- a/tests/playwright-test/babel.spec.ts
+++ b/tests/playwright-test/babel.spec.ts
@@ -148,5 +148,5 @@ test('should not transform external', async ({ runInlineTest }) => {
     `
   });
   expect(result.exitCode).toBe(1);
-  expect(result.output).toContain('Cannot use import statement outside a module');
+  expect(result.output).toMatch(/(Cannot use import statement outside a module|require\(\) of ES Module .* not supported.)/);
 });