diff --git a/packages/google-cloud-iap/setup.py b/packages/google-cloud-iap/setup.py
index 90f139b84686..4d0663827bbc 100644
--- a/packages/google-cloud-iap/setup.py
+++ b/packages/google-cloud-iap/setup.py
@@ -25,7 +25,7 @@
 release_status = "Development Status :: 5 - Production/Stable"
 url = "https://github.com/googleapis/python-iap"
 dependencies = [
-    "google-api-core[grpc] >= 2.8.0, <3.0.0dev",
+    "google-api-core[grpc] >= 1.32.0, <3.0.0dev,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.*,!=2.4.*,!=2.5.*,!=2.6.*,!=2.7.*",
     "proto-plus >= 1.15.0, <2.0.0dev",
     "protobuf >= 3.19.0, <4.0.0dev",
     "grpc-google-iam-v1 >= 0.12.4, <1.0.0dev",
diff --git a/packages/google-cloud-iap/testing/constraints-3.7.txt b/packages/google-cloud-iap/testing/constraints-3.7.txt
index 76a56f7f24bb..acf929dcc3a6 100644
--- a/packages/google-cloud-iap/testing/constraints-3.7.txt
+++ b/packages/google-cloud-iap/testing/constraints-3.7.txt
@@ -4,7 +4,7 @@
 # Pin the version to the lower bound.
 # e.g., if setup.py has "google-cloud-foo >= 1.14.0, < 2.0.0dev",
 # Then this file should have google-cloud-foo==1.14.0
-google-api-core==2.8.0
+google-api-core==1.32.0
 proto-plus==1.15.0
 grpc-google-iam-v1==0.12.4
 protobuf==3.19.0