diff --git a/airflow-core/src/airflow/api/common/mark_tasks.py b/airflow-core/src/airflow/api/common/mark_tasks.py
index 09fa9cd5c5e84..bb7fee0c2bfa9 100644
--- a/airflow-core/src/airflow/api/common/mark_tasks.py
+++ b/airflow-core/src/airflow/api/common/mark_tasks.py
@@ -185,11 +185,12 @@ def get_run_ids(dag: SerializedDAG, run_id: str, future: bool, past: bool, sessi
     elif not dag.timetable.periodic:
         run_ids = [run_id]
     else:
-        dates = [
+        dates = {current_logical_date}
+        dates.update(
             info.logical_date
-            for info in dag.iter_dagrun_infos_between(start_date, end_date, align=False)
+            for info in dag.iter_dagrun_infos_between(start_date, end_date)
             if info.logical_date  # todo: AIP-76 this will not find anything where logical date is null
-        ]
+        )
         run_ids = [dr.run_id for dr in DagRun.find(dag_id=dag.dag_id, logical_date=dates, session=session)]
     return run_ids
 
diff --git a/airflow-core/src/airflow/serialization/definitions/dag.py b/airflow-core/src/airflow/serialization/definitions/dag.py
index ea3009c564542..bfdf02bd3ac35 100644
--- a/airflow-core/src/airflow/serialization/definitions/dag.py
+++ b/airflow-core/src/airflow/serialization/definitions/dag.py
@@ -434,8 +434,6 @@ def iter_dagrun_infos_between(
         self,
         earliest: datetime.datetime | None,
         latest: datetime.datetime,
-        *,
-        align: bool = True,
     ) -> Iterable[DagRunInfo]:
         """
         Yield DagRunInfo using this DAG's timetable between given interval.
@@ -443,17 +441,6 @@ def iter_dagrun_infos_between(
         DagRunInfo instances yielded if their ``logical_date`` is not earlier
         than ``earliest``, nor later than ``latest``. The instances are ordered
         by their ``logical_date`` from earliest to latest.
-
-        If ``align`` is ``False``, the first run will happen immediately on
-        ``earliest``, even if it does not fall on the logical timetable schedule.
-        The default is ``True``.
-
-        Example: A DAG is scheduled to run every midnight (``0 0 * * *``). If
-        ``earliest`` is ``2021-06-03 23:00:00``, the first DagRunInfo would be
-        ``2021-06-03 23:00:00`` if ``align=False``, and ``2021-06-04 00:00:00``
-        if ``align=True``.
-
-        #  see issue https://github.com/apache/airflow/issues/60455
         """
         if isinstance(self.timetable, CronPartitionTimetable):
             # todo: AIP-76 need to update this so that it handles partitions
@@ -481,21 +468,12 @@ def iter_dagrun_infos_between(
             info = None
 
         if info is None:
-            # No runs to be scheduled between the user-supplied timeframe. But
-            # if align=False, "invent" a data interval for the timeframe itself.
-            if not align:
-                yield DagRunInfo.interval(earliest, latest)
             return
 
         if TYPE_CHECKING:
             # todo: AIP-76 after updating this function for partitions, this may not be true
             assert info.data_interval is not None
 
-        # If align=False and earliest does not fall on the timetable's logical
-        # schedule, "invent" a data interval for it.
-        if not align and info.logical_date != earliest:
-            yield DagRunInfo.interval(earliest, info.data_interval.start)
-
         # Generate naturally according to schedule.
         while info is not None:
             yield info
diff --git a/airflow-core/tests/unit/models/test_dag.py b/airflow-core/tests/unit/models/test_dag.py
index 2a45735847ecf..f10eee376c278 100644
--- a/airflow-core/tests/unit/models/test_dag.py
+++ b/airflow-core/tests/unit/models/test_dag.py
@@ -2746,7 +2746,6 @@ def test_iter_dagrun_infos_between(start_date, expected_infos):
     iterator = create_scheduler_dag(dag).iter_dagrun_infos_between(
         earliest=pendulum.instance(start_date),
         latest=pendulum.instance(DEFAULT_DATE),
-        align=True,
     )
     assert expected_infos == list(iterator)
 
@@ -2783,7 +2782,7 @@ def _get_registered_timetable(s):
     ):
         scheduler_dag = create_scheduler_dag(dag)
 
-    iterator = scheduler_dag.iter_dagrun_infos_between(earliest=start, latest=end, align=True)
+    iterator = scheduler_dag.iter_dagrun_infos_between(earliest=start, latest=end)
     with caplog.at_level(logging.ERROR):
         infos = list(iterator)