diff --git a/sky/adaptors/azure.py b/sky/adaptors/azure.py
index 0cadb0b2bd8..3da4febca3e 100644
--- a/sky/adaptors/azure.py
+++ b/sky/adaptors/azure.py
@@ -177,19 +177,24 @@ def get_client(name: str,
                 container_client = blob.ContainerClient.from_container_url(
                     container_url, credential)
                 try:
+                    # Suppress noisy logs from Azure SDK when attempting
+                    # to run exists() on private container without access.
+                    # Reference:
+                    # https://github.com/Azure/azure-sdk-for-python/issues/9422
+                    azure_logger = logging.getLogger('azure')
+                    original_level = azure_logger.getEffectiveLevel()
+                    azure_logger.setLevel(logging.CRITICAL)
                     container_client.exists()
+                    azure_logger.setLevel(original_level)
                     return container_client
                 except exceptions().ClientAuthenticationError as e:
                     # Caught when user attempted to use private container
-                    # without access rights.
+                    # without access rights. Raised error is handled at the
+                    # upstream.
                     # Reference: https://learn.microsoft.com/en-us/troubleshoot/azure/entra/entra-id/app-integration/error-code-aadsts50020-user-account-identity-provider-does-not-exist # pylint: disable=line-too-long
                     if 'ERROR: AADSTS50020' in str(e):
                         with ux_utils.print_exception_no_traceback():
-                            raise sky_exceptions.StorageBucketGetError(
-                                'Attempted to fetch a non-existent public '
-                                'container name: '
-                                f'{container_client.container_name}. '
-                                'Please check if the name is correct.')
+                            raise e
                     with ux_utils.print_exception_no_traceback():
                         raise sky_exceptions.StorageBucketGetError(
                             'Failed to retreive the container client for the '
diff --git a/sky/data/storage.py b/sky/data/storage.py
index b915d1c6d54..b22c4c0da75 100644
--- a/sky/data/storage.py
+++ b/sky/data/storage.py
@@ -2541,11 +2541,22 @@ def _get_bucket(self) -> Tuple[str, bool]:
             container_url = data_utils.AZURE_CONTAINER_URL.format(
                 storage_account_name=self.storage_account_name,
                 container_name=self.name)
-            container_client = data_utils.create_az_client(
-                client_type='container',
-                container_url=container_url,
-                storage_account_name=self.storage_account_name,
-                resource_group_name=self.resource_group_name)
+            try:
+                container_client = data_utils.create_az_client(
+                    client_type='container',
+                    container_url=container_url,
+                    storage_account_name=self.storage_account_name,
+                    resource_group_name=self.resource_group_name)
+            except azure.exceptions().ClientAuthenticationError as e:
+                if 'ERROR: AADSTS50020' in str(e):
+                    # Caught when failing to obtain container client due to
+                    # lack of permission to passed given private container.
+                    if self.resource_group_name is None:
+                        with ux_utils.print_exception_no_traceback():
+                            raise exceptions.StorageBucketGetError(
+                                _BUCKET_FAIL_TO_CONNECT_MESSAGE.format(
+                                    name=self.name))
+                raise
             if container_client.exists():
                 is_private = (True if
                               container_client.get_container_properties().get(
diff --git a/tests/test_smoke.py b/tests/test_smoke.py
index c5d723b8be4..8cd260e0767 100644
--- a/tests/test_smoke.py
+++ b/tests/test_smoke.py
@@ -5069,14 +5069,10 @@ def test_private_bucket(self, private_bucket):
                 private_bucket).path.strip('/')
         else:
             private_bucket_name = urllib.parse.urlsplit(private_bucket).netloc
-        match_str = storage_lib._BUCKET_FAIL_TO_CONNECT_MESSAGE.format(
-            name=private_bucket_name)
-        if store_type == 'https':
-            # Azure blob uses a different error string since container may
-            # not exist even though the bucket name is ok.
-            match_str = 'Attempted to fetch a non-existent public container'
-        with pytest.raises(sky.exceptions.StorageBucketGetError,
-                           match=match_str):
+        with pytest.raises(
+                sky.exceptions.StorageBucketGetError,
+                match=storage_lib._BUCKET_FAIL_TO_CONNECT_MESSAGE.format(
+                    name=private_bucket_name)):
             storage_obj = storage_lib.Storage(source=private_bucket)
 
     @pytest.mark.no_fluidstack