diff --git a/dvc/remote/ssh/connection.py b/dvc/remote/ssh/connection.py
index f8a38a0eb..fa2e8a5ee 100644
--- a/dvc/remote/ssh/connection.py
+++ b/dvc/remote/ssh/connection.py
@@ -194,7 +194,12 @@ class SSHConnection:
         self.makedirs(posixpath.dirname(dst))
 
         tmp = tmp_fname(dst)
-        self.copy(src, tmp)
+
+        try:
+            self.sftp.rename(src, tmp)
+        except OSError:
+            self.copy(src, tmp)
+
         self.sftp.rename(tmp, dst)
         self.remove(src)