diff --git a/dvc/repo/fetch.py b/dvc/repo/fetch.py
index 05f92921d0..047a45f9c9 100644
--- a/dvc/repo/fetch.py
+++ b/dvc/repo/fetch.py
@@ -2,6 +2,7 @@
 
 from dvc.exceptions import DownloadError
 from dvc.log import logger
+from dvc.stage.cache import RunCacheNotSupported
 from dvc.ui import ui
 from dvc_data.index import DataIndex, FileStorage
 
@@ -136,6 +137,8 @@ def fetch(  # noqa: PLR0913
     try:
         if run_cache:
             self.stage_cache.pull(remote)
+    except RunCacheNotSupported as e:
+        logger.debug("failed to pull run cache: %s", e)
     except DownloadError as exc:
         failed_count += exc.amount
 
diff --git a/dvc/repo/push.py b/dvc/repo/push.py
index 202827c836..acf31573ce 100644
--- a/dvc/repo/push.py
+++ b/dvc/repo/push.py
@@ -1,10 +1,14 @@
 from contextlib import suppress
 
 from dvc.exceptions import InvalidArgumentError, UploadError
+from dvc.log import logger
+from dvc.stage.cache import RunCacheNotSupported
 from dvc.ui import ui
 
 from . import locked
 
+logger = logger.getChild(__name__)
+
 
 def _rebuild(idx, path, fs, cb):
     from dvc_data.index import DataIndex, DataIndexEntry, Meta
@@ -95,8 +99,11 @@ def push(  # noqa: PLR0913
                 "Multiple rev push is unsupported for cloud versioned remotes"
             )
 
-    used_run_cache = self.stage_cache.push(remote) if run_cache else []
-    transferred_count += len(used_run_cache)
+    try:
+        used_run_cache = self.stage_cache.push(remote) if run_cache else []
+        transferred_count += len(used_run_cache)
+    except RunCacheNotSupported as e:
+        logger.debug("failed to push run cache: %s", e)
 
     if isinstance(targets, str):
         targets = [targets]
diff --git a/tests/func/test_run_cache.py b/tests/func/test_run_cache.py
index a8669e88bd..495e64c838 100644
--- a/tests/func/test_run_cache.py
+++ b/tests/func/test_run_cache.py
@@ -1,3 +1,4 @@
+import logging
 import os
 
 import pytest
@@ -231,13 +232,15 @@ def test_restore_pull(tmp_dir, dvc, run_copy, mocker, local_remote):
     assert (tmp_dir / LOCK_FILE).exists()
 
 
-def test_push_pull_unsupported(tmp_dir, dvc, mocker, run_copy):
+def test_push_pull_unsupported(tmp_dir, dvc, mocker, run_copy, local_remote, caplog):
     tmp_dir.gen("foo", "foo")
     run_copy("foo", "bar", name="copy-foo-bar")
     mocker.patch.object(
         dvc.cloud, "get_remote_odb", side_effect=RunCacheNotSupported("foo")
     )
-    with pytest.raises(RunCacheNotSupported):
+    with caplog.at_level(logging.DEBUG):
         dvc.push(run_cache=True)
-    with pytest.raises(RunCacheNotSupported):
+        assert "failed to push run cache" in caplog.text
+    with caplog.at_level(logging.DEBUG):
         dvc.pull(run_cache=True)
+        assert "failed to pull run cache" in caplog.text