diff --git a/Jenkinsfile b/Jenkinsfile
index ccb0097481ac..2b318dfbb503 100644
--- a/Jenkinsfile
+++ b/Jenkinsfile
@@ -516,6 +516,11 @@ def getBeatsName(baseDir) {
 */
 def e2e(Map args = [:]) {
   if (!args.e2e?.get('enabled', false)) { return }
+  // Skip running the tests on branches or tags if configured.
+  if (!isPR() && args.e2e?.get('when', false)) {
+    if (isBranch() && !args.e2e.when.get('branches', true)) { return }
+    if (isTag() && !args.e2e.when.get('tags', true)) { return }
+  }
   if (args.e2e.get('entrypoint', '')?.trim()) {
     e2e_with_entrypoint(args)
   } else {
diff --git a/x-pack/elastic-agent/Jenkinsfile.yml b/x-pack/elastic-agent/Jenkinsfile.yml
index 23a5daf0a6f8..3e2155401c55 100644
--- a/x-pack/elastic-agent/Jenkinsfile.yml
+++ b/x-pack/elastic-agent/Jenkinsfile.yml
@@ -98,6 +98,9 @@ stages:
             enabled: true
             job: 'e2e-tests/e2e-testing-mbp'
             testMatrixFile: '.ci/.e2e-tests-for-elastic-agent.yaml'
+            when:                  ## Customise when to run this subtask in the packaging stage.
+                branches: false    ## Only on a PR basis for the time being
+                tags: false        ## e2e on branches/tags is already in place with the downstream build.
         stage: packaging
     packaging-arm:
         packaging-arm: "mage package"