diff --git a/ignite/engine/engine.py b/ignite/engine/engine.py
index 2679e97ccc8f..22406badb2fd 100644
--- a/ignite/engine/engine.py
+++ b/ignite/engine/engine.py
@@ -695,25 +695,32 @@ def _internal_run(self) -> State:
                     self._setup_engine()
 
                 time_taken = self._run_once_on_dataset()
+                # time is available for handlers but must be update after fire
+                self.state.times[Events.EPOCH_COMPLETED.name] = time_taken
+                handlers_start_time = time.time()
+                if self.should_terminate:
+                    self._fire_event(Events.TERMINATE)
+                else:
+                    self._fire_event(Events.EPOCH_COMPLETED)
+                time_taken += time.time() - handlers_start_time
+                # update time wrt handlers
                 self.state.times[Events.EPOCH_COMPLETED.name] = time_taken
                 hours, mins, secs = _to_hours_mins_secs(time_taken)
-                elapsed_time_message = "Epoch[%s] Complete. Time taken: %02d:%02d:%02d" % (
-                    self.state.epoch,
-                    hours,
-                    mins,
-                    secs,
+                self.logger.info(
+                    "Epoch[%s] Complete. Time taken: %02d:%02d:%02d" % (self.state.epoch, hours, mins, secs)
                 )
                 if self.should_terminate:
-                    self._fire_event(Events.TERMINATE)
-                    self.logger.info(elapsed_time_message)
                     break
-                self._fire_event(Events.EPOCH_COMPLETED)
-                self.logger.info(elapsed_time_message)
 
             time_taken = time.time() - start_time
-            hours, mins, secs = _to_hours_mins_secs(time_taken)
+            # time is available for handlers but must be update after fire
             self.state.times[Events.COMPLETED.name] = time_taken
+            handlers_start_time = time.time()
             self._fire_event(Events.COMPLETED)
+            time_taken += time.time() - handlers_start_time
+            # update time wrt handlers
+            self.state.times[Events.COMPLETED.name] = time_taken
+            hours, mins, secs = _to_hours_mins_secs(time_taken)
             self.logger.info("Engine run complete. Time taken: %02d:%02d:%02d" % (hours, mins, secs))
 
         except BaseException as e:
diff --git a/tests/ignite/engine/test_engine.py b/tests/ignite/engine/test_engine.py
index 7c1f0e5d0455..8c2d966b11db 100644
--- a/tests/ignite/engine/test_engine.py
+++ b/tests/ignite/engine/test_engine.py
@@ -377,19 +377,29 @@ def test_state_get_event_attrib_value():
 def test_time_stored_in_state():
     def _test(data, max_epochs, epoch_length):
         sleep_time = 0.01
+        extra_sleep_time = 0.1
         engine = Engine(lambda e, b: time.sleep(sleep_time))
 
-        def check_epoch_time(engine):
+        @engine.on(Events.EPOCH_COMPLETED)
+        def check_epoch_time():
             assert engine.state.times[Events.EPOCH_COMPLETED.name] >= sleep_time * epoch_length
+            time.sleep(extra_sleep_time)
 
-        def check_completed_time(engine):
-            assert engine.state.times[Events.COMPLETED.name] >= sleep_time * epoch_length * max_epochs
-
-        engine.add_event_handler(Events.EPOCH_COMPLETED, lambda e: check_epoch_time(e))
-        engine.add_event_handler(Events.COMPLETED, lambda e: check_completed_time(e))
+        @engine.on(Events.COMPLETED)
+        def check_completed_time():
+            assert (
+                engine.state.times[Events.COMPLETED.name] >= (sleep_time * epoch_length + extra_sleep_time) * max_epochs
+            )
+            time.sleep(extra_sleep_time)
 
         engine.run(data, max_epochs=max_epochs, epoch_length=epoch_length)
 
+        assert engine.state.times[Events.EPOCH_COMPLETED.name] >= sleep_time * epoch_length + extra_sleep_time
+        assert (
+            engine.state.times[Events.COMPLETED.name]
+            >= (sleep_time * epoch_length + extra_sleep_time) * max_epochs + extra_sleep_time
+        )
+
     _test(list(range(100)), max_epochs=2, epoch_length=100)
     _test(list(range(200)), max_epochs=2, epoch_length=100)
     _test(list(range(200)), max_epochs=5, epoch_length=100)