diff --git a/task-sdk/src/airflow/sdk/execution_time/task_runner.py b/task-sdk/src/airflow/sdk/execution_time/task_runner.py
index 822ed9bb50ae8..461e770c42501 100644
--- a/task-sdk/src/airflow/sdk/execution_time/task_runner.py
+++ b/task-sdk/src/airflow/sdk/execution_time/task_runner.py
@@ -1395,9 +1395,17 @@ def finalize(
     task = ti.task
     # Pushing xcom for each operator extra links defined on the operator only.
     for oe in task.operator_extra_links:
-        link, xcom_key = oe.get_link(operator=task, ti_key=ti), oe.xcom_key  # type: ignore[arg-type]
-        log.debug("Setting xcom for operator extra link", link=link, xcom_key=xcom_key)
-        _xcom_push_to_db(ti, key=xcom_key, value=link)
+        try:
+            link, xcom_key = oe.get_link(operator=task, ti_key=ti), oe.xcom_key  # type: ignore[arg-type]
+            log.debug("Setting xcom for operator extra link", link=link, xcom_key=xcom_key)
+            _xcom_push_to_db(ti, key=xcom_key, value=link)
+        except Exception:
+            log.exception(
+                "Failed to push an xcom for task operator extra link",
+                link_name=oe.name,
+                xcom_key=oe.xcom_key,
+                ti=ti,
+            )
 
     if getattr(ti.task, "overwrite_rtif_after_execution", False):
         log.debug("Overwriting Rendered template fields.")
diff --git a/task-sdk/tests/task_sdk/execution_time/test_task_runner.py b/task-sdk/tests/task_sdk/execution_time/test_task_runner.py
index 58dda3371ef1d..4adf3c23723fb 100644
--- a/task-sdk/tests/task_sdk/execution_time/test_task_runner.py
+++ b/task-sdk/tests/task_sdk/execution_time/test_task_runner.py
@@ -27,7 +27,7 @@
 from pathlib import Path
 from typing import TYPE_CHECKING
 from unittest import mock
-from unittest.mock import patch
+from unittest.mock import call, patch
 
 import pandas as pd
 import pytest
@@ -48,6 +48,7 @@
 from airflow.sdk import (
     DAG,
     BaseOperator,
+    BaseOperatorLink,
     Connection,
     dag as dag_decorator,
     get_current_context,
@@ -1723,6 +1724,93 @@ def execute(self, context):
                 map_index=runtime_ti.map_index,
             )
 
+    def test_task_failed_with_operator_extra_links(
+        self, create_runtime_ti, mock_supervisor_comms, time_machine
+    ):
+        """Test that operator extra links are pushed to xcoms even when task fails."""
+        instant = timezone.datetime(2024, 12, 3, 10, 0)
+        time_machine.move_to(instant, tick=False)
+
+        class DummyTestOperator(BaseOperator):
+            operator_extra_links = (AirflowLink(),)
+
+            def execute(self, context):
+                raise ValueError("Task failed intentionally")
+
+        task = DummyTestOperator(task_id="task_with_operator_extra_links")
+        runtime_ti = create_runtime_ti(task=task)
+        context = runtime_ti.get_template_context()
+        runtime_ti.start_date = instant
+        runtime_ti.end_date = instant
+
+        state, _, error = run(runtime_ti, context=context, log=mock.MagicMock())
+        assert state == TaskInstanceState.FAILED
+        assert error is not None
+
+        with mock.patch.object(XCom, "_set_xcom_in_db") as mock_xcom_set:
+            finalize(
+                runtime_ti,
+                log=mock.MagicMock(),
+                state=TaskInstanceState.FAILED,
+                context=context,
+                error=error,
+            )
+            assert mock_xcom_set.mock_calls == [
+                call(
+                    key="_link_AirflowLink",
+                    value="https://airflow.apache.org",
+                    dag_id=runtime_ti.dag_id,
+                    task_id=runtime_ti.task_id,
+                    run_id=runtime_ti.run_id,
+                    map_index=runtime_ti.map_index,
+                )
+            ]
+
+    def test_operator_extra_links_exception_handling(
+        self, create_runtime_ti, mock_supervisor_comms, time_machine
+    ):
+        """Test that exceptions in get_link() don't prevent other links from being pushed."""
+        instant = timezone.datetime(2024, 12, 3, 10, 0)
+        time_machine.move_to(instant, tick=False)
+
+        class FailingLink(BaseOperatorLink):
+            """A link that raises an exception when get_link is called."""
+
+            name = "failing_link"
+
+            def get_link(self, operator, *, ti_key):
+                raise ValueError("Link generation failed")
+
+        class DummyTestOperator(BaseOperator):
+            operator_extra_links = (FailingLink(), AirflowLink())
+
+            def execute(self, context):
+                pass
+
+        task = DummyTestOperator(task_id="task_with_multiple_links")
+        runtime_ti = create_runtime_ti(task=task)
+        context = runtime_ti.get_template_context()
+        runtime_ti.start_date = instant
+        runtime_ti.end_date = instant
+
+        with mock.patch.object(XCom, "_set_xcom_in_db") as mock_xcom_set:
+            finalize(
+                runtime_ti,
+                log=mock.MagicMock(),
+                state=TaskInstanceState.SUCCESS,
+                context=context,
+            )
+            assert mock_xcom_set.mock_calls == [
+                call(
+                    key="_link_AirflowLink",
+                    value="https://airflow.apache.org",
+                    dag_id=runtime_ti.dag_id,
+                    task_id=runtime_ti.task_id,
+                    run_id=runtime_ti.run_id,
+                    map_index=runtime_ti.map_index,
+                )
+            ]
+
     @pytest.mark.parametrize(
         ["cmd", "rendered_cmd"],
         [