diff --git a/airflow/providers/amazon/aws/log/s3_task_handler.py b/airflow/providers/amazon/aws/log/s3_task_handler.py
index 831c86417185f..098f17a28a95c 100644
--- a/airflow/providers/amazon/aws/log/s3_task_handler.py
+++ b/airflow/providers/amazon/aws/log/s3_task_handler.py
@@ -128,8 +128,12 @@ def _read(self, ti, try_number, metadata=None):
         if logs:
             return "".join(f"*** {x}\n" for x in messages) + "\n".join(logs), {"end_of_log": True}
         else:
+            if metadata and metadata.get("log_pos", 0) > 0:
+                log_prefix = ""
+            else:
+                log_prefix = "*** Falling back to local log\n"
             local_log, metadata = super()._read(ti, try_number, metadata)
-            return "*** Falling back to local log\n" + local_log, metadata
+            return f"{log_prefix}{local_log}", metadata
 
     def s3_log_exists(self, remote_log_location: str) -> bool:
         """
diff --git a/tests/providers/amazon/aws/log/test_s3_task_handler.py b/tests/providers/amazon/aws/log/test_s3_task_handler.py
index 4fbe453274a9b..aeca09d36d6a7 100644
--- a/tests/providers/amazon/aws/log/test_s3_task_handler.py
+++ b/tests/providers/amazon/aws/log/test_s3_task_handler.py
@@ -146,6 +146,33 @@ def test_read_when_s3_log_missing(self):
         assert actual == expected
         assert {"end_of_log": True, "log_pos": 0} == metadata[0]
 
+    def test_read_when_s3_log_missing_and_log_pos_missing_pre_26(self):
+        ti = copy.copy(self.ti)
+        ti.state = TaskInstanceState.SUCCESS
+        # mock that super class has no _read_remote_logs method
+        with mock.patch("airflow.providers.amazon.aws.log.s3_task_handler.hasattr", return_value=False):
+            log, metadata = self.s3_task_handler.read(ti)
+        assert 1 == len(log)
+        assert log[0][0][-1].startswith("*** Falling back to local log")
+
+    def test_read_when_s3_log_missing_and_log_pos_zero_pre_26(self):
+        ti = copy.copy(self.ti)
+        ti.state = TaskInstanceState.SUCCESS
+        # mock that super class has no _read_remote_logs method
+        with mock.patch("airflow.providers.amazon.aws.log.s3_task_handler.hasattr", return_value=False):
+            log, metadata = self.s3_task_handler.read(ti, metadata={"log_pos": 0})
+        assert 1 == len(log)
+        assert log[0][0][-1].startswith("*** Falling back to local log")
+
+    def test_read_when_s3_log_missing_and_log_pos_over_zero_pre_26(self):
+        ti = copy.copy(self.ti)
+        ti.state = TaskInstanceState.SUCCESS
+        # mock that super class has no _read_remote_logs method
+        with mock.patch("airflow.providers.amazon.aws.log.s3_task_handler.hasattr", return_value=False):
+            log, metadata = self.s3_task_handler.read(ti, metadata={"log_pos": 1})
+        assert 1 == len(log)
+        assert not log[0][0][-1].startswith("*** Falling back to local log")
+
     def test_s3_read_when_log_missing(self):
         handler = self.s3_task_handler
         url = "s3://bucket/foo"