diff --git a/packages/google-cloud-appengine-admin/setup.py b/packages/google-cloud-appengine-admin/setup.py
index 150c2f61d53b..73a82cf486e5 100644
--- a/packages/google-cloud-appengine-admin/setup.py
+++ b/packages/google-cloud-appengine-admin/setup.py
@@ -28,7 +28,7 @@
     # NOTE: Maintainers, please do not require google-api-core>=2.x.x
     # Until this issue is closed
     # https://github.com/googleapis/google-cloud-python/issues/10566
-    "google-api-core[grpc] >= 1.28.0, <3.0.0dev",
+    "google-api-core[grpc] >= 1.31.5, <3.0.0dev,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.0",
     "proto-plus >= 1.18.1",
     "grpc-google-iam-v1",
     "six",
diff --git a/packages/google-cloud-appengine-admin/testing/constraints-3.6.txt b/packages/google-cloud-appengine-admin/testing/constraints-3.6.txt
index f4ff37046155..64d95bb2d6b1 100644
--- a/packages/google-cloud-appengine-admin/testing/constraints-3.6.txt
+++ b/packages/google-cloud-appengine-admin/testing/constraints-3.6.txt
@@ -5,7 +5,7 @@
 #
 # e.g., if setup.py has "foo >= 1.14.0, < 2.0.0dev",
 # Then this file should have foo==1.14.0
-google-api-core==1.28.0
+google-api-core==1.31.5
 proto-plus==1.18.1
 grpc-google-iam-v1==0.12.3
 six==1.13.0