diff --git a/scripts/release-version.mjs b/scripts/release-version.mjs
index 9b522972..a5da62e9 100644
--- a/scripts/release-version.mjs
+++ b/scripts/release-version.mjs
@@ -101,6 +101,22 @@ function getLocalDatePart() {
  * @returns {string|null}
  */
 function getRunIdentifier() {
+  const runNumber = process.env.GITHUB_RUN_NUMBER;
+  if (runNumber && /^[0-9]+$/.test(runNumber)) {
+    const runNum = Number.parseInt(runNumber, 10);
+    if (!Number.isNaN(runNum)) {
+      const base = `r${runNum.toString(36)}`;
+      const attempt = process.env.GITHUB_RUN_ATTEMPT;
+      if (attempt && /^[0-9]+$/.test(attempt)) {
+        const attemptNumber = Number.parseInt(attempt, 10);
+        if (!Number.isNaN(attemptNumber) && attemptNumber > 1) {
+          return `${base}${attemptNumber.toString(36)}`;
+        }
+      }
+      return base;
+    }
+  }
+
   const attempt = process.env.GITHUB_RUN_ATTEMPT;
   if (attempt && /^[0-9]+$/.test(attempt)) {
     const attemptNumber = Number.parseInt(attempt, 10);
@@ -109,14 +125,6 @@ function getRunIdentifier() {
     }
   }
 
-  const runNumber = process.env.GITHUB_RUN_NUMBER;
-  if (runNumber && /^[0-9]+$/.test(runNumber)) {
-    const runNum = Number.parseInt(runNumber, 10);
-    if (!Number.isNaN(runNum)) {
-      return `r${runNum.toString(36)}`;
-    }
-  }
-
   return null;
 }