diff --git a/CHANGELOG.md b/CHANGELOG.md
index 61fb9d7039..6c74cc13b8 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -209,6 +209,12 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 - Fixed an issue with `IterableDataset` when `__len__` is not defined ([#6828](https://github.com/PyTorchLightning/pytorch-lightning/pull/6828))
 
 
+- Fixed `EarlyStopping` logic when `min_epochs` or `min_steps` requirement is not met ([#6705](https://github.com/PyTorchLightning/pytorch-lightning/pull/6705))
+
+
+- Fixed a bug where `TensorBoardLogger` would give a warning and not log correctly to a symbolic link `save_dir` ([#6730](https://github.com/PyTorchLightning/pytorch-lightning/pull/6730))
+
+
 ## [1.2.6] - 2021-03-30
 
 ### Changed
@@ -241,12 +247,8 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 - Fixed comparing required versions ([#6434](https://github.com/PyTorchLightning/pytorch-lightning/pull/6434))
 - Fixed duplicate logs appearing in console when using the python logging module ([#6275](https://github.com/PyTorchLightning/pytorch-lightning/pull/6275))
 - Added Autocast in validation, test and predict modes for Native AMP ([#6565](https://github.com/PyTorchLightning/pytorch-lightning/pull/6565))
-
-
 - Fixed resolve a bug with omegaconf and xm.save ([#6741](https://github.com/PyTorchLightning/pytorch-lightning/pull/6741))
 
-- Fixed a bug where `TensorBoardLogger` would give a warning and not log correctly to a symbolic link `save_dir` ([#6730](https://github.com/PyTorchLightning/pytorch-lightning/pull/6730))
-
 
 ## [1.2.4] - 2021-03-16
 
diff --git a/pytorch_lightning/trainer/trainer.py b/pytorch_lightning/trainer/trainer.py
index 27dcd6fe9a..36b591ba4e 100644
--- a/pytorch_lightning/trainer/trainer.py
+++ b/pytorch_lightning/trainer/trainer.py
@@ -614,6 +614,7 @@ class Trainer(
                             f' ({self.min_epochs}) or minimum steps ({self.min_steps}) has'
                             ' not been met. Training will continue...'
                         )
+                        self.should_stop = False
 
             # hook
             self.train_loop.on_train_end()
diff --git a/tests/trainer/test_trainer.py b/tests/trainer/test_trainer.py
index 0c0488009d..bab26522ea 100644
--- a/tests/trainer/test_trainer.py
+++ b/tests/trainer/test_trainer.py
@@ -11,6 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
+import logging
 import math
 import os
 import pickle
@@ -528,6 +529,40 @@ def test_trainer_min_steps_and_epochs(tmpdir):
     assert trainer.global_step >= math.floor(num_train_samples * 1.5), "Model did not train for at least min_steps"
 
 
+def test_trainer_min_steps_and_min_epochs_not_reached(tmpdir, caplog):
+    """ Test that min_epochs/min_steps in Trainer are enforced even if EarlyStopping is triggered. """
+
+    class TestModel(BoringModel):
+        training_step_invoked = 0
+
+        def training_step(self, batch, batch_idx):
+            output = super().training_step(batch, batch_idx)
+            output["loss"] = output["loss"] * 0.0  # force minimal loss to trigger early stopping
+            self.log("loss", output["loss"])
+            self.training_step_invoked += 1
+            assert not self.trainer.should_stop
+            return output
+
+    model = TestModel()
+    early_stop = EarlyStopping(monitor="loss", patience=0)
+    min_epochs = 5
+    trainer = Trainer(
+        default_root_dir=tmpdir,
+        progress_bar_refresh_rate=0,
+        min_epochs=min_epochs,
+        limit_val_batches=0,
+        limit_train_batches=2,
+        callbacks=[early_stop]
+    )
+    with caplog.at_level(logging.INFO, logger="pytorch_lightning.trainer.trainer"):
+        trainer.fit(model)
+
+    message = f"minimum epochs ({min_epochs}) or minimum steps (None) has not been met. Training will continue"
+    num_messages = len([record.message for record in caplog.records if message in record.message])
+    assert num_messages == min_epochs - 2
+    assert model.training_step_invoked == min_epochs * 2
+
+
 def test_trainer_max_steps_accumulate_batches(tmpdir):
     """Verify model trains according to specified max steps with grad accumulated batches"""
     model = BoringModel()