diff --git a/google/api_core/operations_v1/abstract_operations_base_client.py b/google/api_core/operations_v1/abstract_operations_base_client.py
index 160c2a88..f62f60b0 100644
--- a/google/api_core/operations_v1/abstract_operations_base_client.py
+++ b/google/api_core/operations_v1/abstract_operations_base_client.py
@@ -300,16 +300,22 @@ def __init__(
             client_options = client_options_lib.ClientOptions()
 
         # Create SSL credentials for mutual TLS if needed.
-        use_client_cert = os.getenv(
-            "GOOGLE_API_USE_CLIENT_CERTIFICATE", "false"
-        ).lower()
-        if use_client_cert not in ("true", "false"):
-            raise ValueError(
-                "Environment variable `GOOGLE_API_USE_CLIENT_CERTIFICATE` must be either `true` or `false`"
-            )
+        if hasattr(mtls, "should_use_client_cert"):
+            use_client_cert = mtls.should_use_client_cert()
+        else:
+            # if unsupported, fallback to reading from env var
+            use_client_cert_str = os.getenv(
+                "GOOGLE_API_USE_CLIENT_CERTIFICATE", "false"
+            ).lower()
+            if use_client_cert_str not in ("true", "false"):
+                raise ValueError(
+                    "Environment variable `GOOGLE_API_USE_CLIENT_CERTIFICATE` must be"
+                    " either `true` or `false`"
+                )
+            use_client_cert = use_client_cert_str == "true"
         client_cert_source_func = None
         is_mtls = False
-        if use_client_cert == "true":
+        if use_client_cert:
             if client_options.client_cert_source:
                 is_mtls = True
                 client_cert_source_func = client_options.client_cert_source
diff --git a/tests/unit/operations_v1/test_operations_rest_client.py b/tests/unit/operations_v1/test_operations_rest_client.py
index 87523c5d..e513db7a 100644
--- a/tests/unit/operations_v1/test_operations_rest_client.py
+++ b/tests/unit/operations_v1/test_operations_rest_client.py
@@ -35,6 +35,7 @@
 from google.api_core import client_options
 from google.api_core import exceptions as core_exceptions
 from google.api_core import gapic_v1
+from google.api_core import parse_version_to_tuple
 from google.api_core.operations_v1 import AbstractOperationsClient
 
 import google.auth
@@ -42,6 +43,7 @@
 from google.api_core.operations_v1 import pagers_async
 from google.api_core.operations_v1 import transports
 from google.auth import credentials as ga_credentials
+from google.auth import __version__ as auth_version
 from google.auth.exceptions import MutualTLSChannelError
 from google.longrunning import operations_pb2
 from google.oauth2 import service_account
@@ -346,12 +348,30 @@ def test_operations_client_client_options(
         with pytest.raises(MutualTLSChannelError):
             client = client_class()
 
-    # Check the case GOOGLE_API_USE_CLIENT_CERTIFICATE has unsupported value.
+    # Check the case GOOGLE_API_USE_CLIENT_CERTIFICATE has unsupported value
     with mock.patch.dict(
         os.environ, {"GOOGLE_API_USE_CLIENT_CERTIFICATE": "Unsupported"}
     ):
-        with pytest.raises(ValueError):
-            client = client_class()
+        # Test behavior for google.auth versions < 2.43.0.
+        # These versions do not have the updated mtls.should_use_client_cert logic.
+        # Verify that a ValueError is raised when GOOGLE_API_USE_CLIENT_CERTIFICATE
+        # is set to an unsupported value, as expected in these older versions.
+        if parse_version_to_tuple(auth_version) < (2, 43, 0):
+            with pytest.raises(ValueError):
+                client = client_class()
+        # Test behavior for google.auth versions >= 2.43.0.
+        # In these versions, if GOOGLE_API_USE_CLIENT_CERTIFICATE is set to an
+        # unsupported value (e.g., not 'true' or 'false'), the expected behavior
+        # of the internal google.auth.mtls.should_use_client_cert() function
+        # is to return False. Expect should_use_client_cert to return False, so
+        # client creation should proceed without requiring a client certificate.
+        else:
+            with mock.patch.object(transport_class, "__init__") as patched:
+                patched.return_value = None
+                client = client_class(
+                    credentials=ga_credentials.AnonymousCredentials(),
+                    transport=transport_name,
+                )
 
     # Check the case quota_project_id is provided
     options = client_options.ClientOptions(quota_project_id="octopus")