diff --git a/packages/e2e-test-utils/src/click-on-more-menu-item.js b/packages/e2e-test-utils/src/click-on-more-menu-item.js
index a71cf13f1e12c..0465441ec6496 100644
--- a/packages/e2e-test-utils/src/click-on-more-menu-item.js
+++ b/packages/e2e-test-utils/src/click-on-more-menu-item.js
@@ -1,3 +1,8 @@
+/**
+ * External dependencies
+ */
+import { first } from 'lodash';
+
 /**
  * Clicks on More Menu item, searches for the button with the text provided and clicks it.
  *
@@ -7,7 +12,18 @@ export async function clickOnMoreMenuItem( buttonLabel ) {
 	await expect( page ).toClick(
 		'.edit-post-more-menu [aria-label="Show more tools & options"]'
 	);
-	await page.click(
-		`.edit-post-more-menu__content button[aria-label="${ buttonLabel }"]`
-	);
+	const moreMenuContainerSelector =
+		'//*[contains(concat(" ", @class, " "), " edit-post-more-menu__content ")]';
+	let elementToClick = first( await page.$x(
+		`${ moreMenuContainerSelector }//button[contains(text(), "${ buttonLabel }")]`
+	) );
+	// If button is not found, the label should be on the info wrapper.
+	if ( ! elementToClick ) {
+		elementToClick = first( await page.$x(
+			moreMenuContainerSelector +
+			'//button' +
+			`/*[contains(concat(" ", @class, " "), " components-menu-item__info-wrapper ")][contains(text(), "${ buttonLabel }")]`
+		) );
+	}
+	await elementToClick.click();
 }