diff --git a/ignite/engine/engine.py b/ignite/engine/engine.py
index f3f95c9a2e27..c814f770e77a 100644
--- a/ignite/engine/engine.py
+++ b/ignite/engine/engine.py
@@ -1069,7 +1069,7 @@ def _run_once_on_dataset_as_gen(self) -> Generator[State, None, float]:
                 )
 
             while True:
-                self.state.batch = self.state.output = None
+                self.state.batch = None
 
                 try:
                     # Avoid Events.GET_BATCH_STARTED triggered twice when data iter is restarted
@@ -1081,6 +1081,9 @@ def _run_once_on_dataset_as_gen(self) -> Generator[State, None, float]:
                             yield from self._maybe_terminate_or_interrupt()
 
                     self.state.batch = next(self._dataloader_iter)
+                    # We on purpose reset state.output here as for iterable dataloaders
+                    # we accidentally can remove it when one epoch is completed.
+                    self.state.output = None
 
                     # We should not trigger GET_BATCH_STARTED, GET_BATCH_COMPLETED, DATALOADER_STOP_ITERATION events
                     # if no data was provided to engine.run(data=None, ...)
@@ -1254,7 +1257,7 @@ def _run_once_on_dataset_legacy(self) -> float:
                 )
 
             while True:
-                self.state.batch = self.state.output = None
+                self.state.batch = None
                 try:
                     # Avoid Events.GET_BATCH_STARTED triggered twice when data iter is restarted
                     if self.last_event_name != Events.DATALOADER_STOP_ITERATION:
@@ -1265,6 +1268,10 @@ def _run_once_on_dataset_legacy(self) -> float:
                             self._maybe_terminate_legacy()
 
                     self.state.batch = next(self._dataloader_iter)
+                    # We on purpose reset state.output here as for iterable dataloaders
+                    # we accidentally can remove it when one epoch is completed.
+                    self.state.output = None
+
                     # We should not trigger GET_BATCH_STARTED, GET_BATCH_COMPLETED, DATALOADER_STOP_ITERATION events
                     # if no data was provided to engine.run(data=None, ...)
                     if self.state.dataloader is not None:
diff --git a/tests/ignite/engine/test_engine.py b/tests/ignite/engine/test_engine.py
index 76e1ad837605..8748e03f574c 100644
--- a/tests/ignite/engine/test_engine.py
+++ b/tests/ignite/engine/test_engine.py
@@ -1279,6 +1279,44 @@ def check_iter_epoch(first_epoch_iter):
         assert engine.state.epoch == 10
         assert engine.state.iteration == 10 * real_epoch_length
 
+    def test_iterator_state_output(self):
+        torch.manual_seed(12)
+
+        def finite_iterator(length, batch_size):
+            for _ in range(length):
+                batch = torch.rand(batch_size, 3, 32, 32)
+                yield batch
+
+        def train_step(trainer, batch):
+            s = trainer.state
+            print(f"{s.epoch}/{s.max_epochs} : {s.iteration} - {batch.norm():.3f}")
+            return "flag_value"
+
+        trainer = Engine(train_step)
+        trainer.run(finite_iterator(4, 4), max_epochs=2)
+
+        assert trainer.state.output == "flag_value"
+        assert trainer.state.epoch == 2
+        # assert trainer.state.iteration == 2*4
+
+    def test_map_state_output(self):
+        torch.manual_seed(12)
+
+        batch_size = 4
+        finite_map = [torch.rand(batch_size, 3, 32, 32) for _ in range(4)]
+
+        def train_step(trainer, batch):
+            s = trainer.state
+            print(f"{s.epoch}/{s.max_epochs} : {s.iteration} - {batch.norm():.3f}")
+            return "flag_value"
+
+        trainer = Engine(train_step)
+        trainer.run(finite_map, max_epochs=2)
+
+        assert trainer.state.output == "flag_value"
+        assert trainer.state.epoch == 2
+        assert trainer.state.iteration == 2 * 4
+
 
 @pytest.mark.parametrize(
     "interrupt_event, e, i",