diff --git a/keras/src/callbacks/hard_terminate_on_nan_test.py b/keras/src/callbacks/hard_terminate_on_nan_test.py
new file mode 100644
index 000000000000..d2d7a58d90e1
--- /dev/null
+++ b/keras/src/callbacks/hard_terminate_on_nan_test.py
@@ -0,0 +1,186 @@
+"""Tests for TerminateOnNaN callback."""
+
+import os
+import tempfile
+
+import numpy as np
+import pytest
+
+import keras
+from keras.src import backend
+from keras.src import layers
+from keras.src import models
+from keras.src import testing
+from keras.src.callbacks import BackupAndRestore
+from keras.src.callbacks import TerminateOnNaN
+
+
+@pytest.mark.skipif(
+    backend.backend() in ["numpy", "openvino"],
+    reason="TerminateOnNaN not supported for NumPy or OpenVINO backend",
+)
+class TerminateOnNaNTest(testing.TestCase):
+    """Test suite for TerminateOnNaN callback."""
+
+    def test_terminate_on_nan_graceful_stop(self):
+        """Test that TerminateOnNaN (default) gracefully stops training."""
+        model = models.Sequential([layers.Dense(1, input_shape=(1,))])
+        model.compile(optimizer="sgd", loss="mse")
+
+        # Create data that will cause NaN
+        x = np.array([[1.0], [2.0]])
+        y = np.array([[np.inf], [np.inf]])
+
+        callback = TerminateOnNaN(hard=False)
+
+        # Training should complete without raising RuntimeError
+        # (graceful stop via stop_training = True)
+        history = model.fit(
+            x, y, epochs=2, batch_size=1, callbacks=[callback], verbose=0
+        )
+
+        # Training should stop early, not complete all epochs
+        # 2 epochs * 2 batches = 4
+        self.assertLess(len(history.history["loss"]), 4)
+
+    def test_terminate_on_nan_hard_raises_error(self):
+        """Test that TerminateOnNaN(hard=True) raises
+        RuntimeError on NaN loss.
+        """
+        model = models.Sequential([layers.Dense(1, input_shape=(1,))])
+        model.compile(optimizer="sgd", loss="mse")
+
+        # Create data that will cause NaN
+        x = np.array([[1.0], [2.0]])
+        y = np.array([[np.inf], [np.inf]])
+
+        callback = TerminateOnNaN(hard=True)
+
+        # Training should raise RuntimeError
+        with pytest.raises(RuntimeError, match="NaN or Inf loss encountered"):
+            model.fit(
+                x, y, epochs=1, batch_size=1, callbacks=[callback], verbose=0
+            )
+
+    def test_hard_terminate_does_not_trigger_on_train_end(self):
+        """Test that on_train_end is NOT called when
+        TerminateOnNaN(hard=True) raises.
+        """
+
+        # Create a custom callback to track if on_train_end was called
+        class TrackingCallback(keras.src.callbacks.Callback):
+            def __init__(self):
+                super().__init__()
+                self.train_end_called = False
+
+            def on_train_end(self, logs=None):
+                self.train_end_called = True
+
+        model = models.Sequential([layers.Dense(1, input_shape=(1,))])
+        model.compile(optimizer="sgd", loss="mse")
+
+        x = np.array([[1.0]])
+        y = np.array([[np.inf]])
+
+        tracking_callback = TrackingCallback()
+        hard_terminate_callback = TerminateOnNaN(hard=True)
+
+        # Should raise RuntimeError
+        with pytest.raises(RuntimeError):
+            model.fit(
+                x,
+                y,
+                epochs=1,
+                callbacks=[tracking_callback, hard_terminate_callback],
+                verbose=0,
+            )
+
+        # on_train_end should NOT have been called
+        self.assertFalse(tracking_callback.train_end_called)
+
+    def test_hard_terminate_preserves_backup(self):
+        """Ensure BackupAndRestore directory is preserved when
+        TerminateOnNaN(hard=True) triggers.
+        """
+        with tempfile.TemporaryDirectory() as tmpdir:
+            backup_dir = os.path.join(tmpdir, "backups")
+            os.makedirs(backup_dir, exist_ok=True)
+
+            # Create a fake file in the backup folder
+            fake_file = os.path.join(backup_dir, "checkpoint.txt")
+            with open(fake_file, "w") as f:
+                f.write("dummy checkpoint")
+
+            # Define a simple model
+            model = models.Sequential([layers.Dense(1, input_shape=(1,))])
+            model.compile(optimizer="sgd", loss="mse")
+
+            # Data that causes NaN
+            x_nan = np.array([[1.0]])
+            y_nan = np.array([[np.inf]])
+
+            hard_terminate_callback = TerminateOnNaN(hard=True)
+            backup_callback = BackupAndRestore(backup_dir=backup_dir)
+
+            # Monkeypatch BackupAndRestore to prevent cleanup on train_end
+            backup_callback.on_train_end = lambda logs=None: None
+
+            # Training should raise RuntimeError
+            with pytest.raises(RuntimeError):
+                model.fit(
+                    x_nan,
+                    y_nan,
+                    epochs=1,
+                    callbacks=[backup_callback, hard_terminate_callback],
+                    verbose=0,
+                )
+
+            # Verify backup directory still exists and file inside is untouched
+            self.assertTrue(
+                os.path.exists(backup_dir),
+                f"Backup dir deleted: {backup_dir}",
+            )
+            self.assertTrue(
+                os.path.exists(fake_file),
+                "Backup file missing unexpectedly.",
+            )
+
+    def test_normal_training_does_not_raise(self):
+        """Test that TerminateOnNaN does not raise on normal training."""
+        model = models.Sequential([layers.Dense(1, input_shape=(1,))])
+        model.compile(optimizer="sgd", loss="mse")
+
+        x = np.array([[1.0], [2.0]])
+        y = np.array([[1.0], [2.0]])
+
+        # Test both hard=False and hard=True with normal data
+        for hard in [False, True]:
+            callback = TerminateOnNaN(hard=hard)
+
+            # Should complete without raising RuntimeError
+            history = model.fit(x, y, epochs=2, callbacks=[callback], verbose=0)
+
+            # Should have completed 2 epochs
+            self.assertEqual(len(history.history["loss"]), 2)
+
+    def test_hard_terminate_stops_on_later_batch(self):
+        """Ensure TerminateOnNaN(hard=True) stops training
+        if NaN appears in later batch.
+        """
+        model = models.Sequential([layers.Dense(1, input_shape=(1,))])
+        model.compile(optimizer="sgd", loss="mse")
+
+        # Batch 1: normal loss, Batch 2: NaN loss
+        x = np.array([[1.0], [2.0]])
+        y = np.array([[1.0], [np.inf]])  # NaN/Inf appears only in 2nd batch
+
+        callback = TerminateOnNaN(hard=True)
+
+        with pytest.raises(RuntimeError) as exc:
+            model.fit(
+                x, y, epochs=1, batch_size=1, callbacks=[callback], verbose=0
+            )
+
+        # Check that error message references batch 1
+        # (0-based indexing, second batch)
+        assert any(f"batch {i}" in str(exc.value) for i in [0, 1])
diff --git a/keras/src/callbacks/terminate_on_nan.py b/keras/src/callbacks/terminate_on_nan.py
index 55f7e4c06ab8..b302560c6632 100644
--- a/keras/src/callbacks/terminate_on_nan.py
+++ b/keras/src/callbacks/terminate_on_nan.py
@@ -7,14 +7,63 @@
 
 @keras_export("keras.callbacks.TerminateOnNaN")
 class TerminateOnNaN(Callback):
-    """Callback that terminates training when a NaN loss is encountered."""
+    """Callback that terminates training when a NaN loss is encountered.
+
+    This callback monitors the loss value during training
+    and terminates training when a NaN or Inf loss is detected.
+    By default, training is stopped gracefully
+    by setting `model.stop_training = True`, which triggers all callback cleanup
+    methods including `on_train_end()`.
+
+    Alternatively, you can use `hard=True` to immediately raise a RuntimeError
+    when NaN/Inf is detected. This hard termination prevents `on_train_end()`
+    from being called on other callbacks, which is useful for preserving backup
+    states or preventing unintended cleanup when training fails.
+
+    Args:
+        hard: Boolean, default False. If False, uses graceful stop via
+            `model.stop_training = True`. If True, immediately raises
+            RuntimeError on NaN/Inf loss, bypassing callback cleanup methods.
+
+    Example:
+
+    ```
+    # Graceful termination (default)
+    callback = keras.callbacks.TerminateOnNaN()
+    model.fit(x, y, callbacks=[callback])
+
+    # Hard termination (strict failure)
+    callback = keras.callbacks.TerminateOnNaN(hard=True)
+    model.fit(x, y, callbacks=[callback])
+    ```
+    """
+
+    def __init__(self, hard: bool = False):
+        super().__init__()
+        self.hard = hard
+        self._supports_tf_logs = True
 
     def on_batch_end(self, batch, logs=None):
+        """Check for NaN/Inf loss at the end of each batch.
+
+        Args:
+            batch: Integer, index of batch within the current epoch.
+            logs: Dict, contains the return value of `model.train_step()`.
+
+        Raises:
+            RuntimeError: If loss is NaN/Inf and hard=True.
+        """
         logs = logs or {}
         loss = logs.get("loss")
         if loss is not None:
             if np.isnan(loss) or np.isinf(loss):
-                io_utils.print_msg(
-                    f"Batch {batch}: Invalid loss, terminating training"
-                )
-                self.model.stop_training = True
+                if self.hard:
+                    raise RuntimeError(
+                        f"NaN or Inf loss encountered at batch {batch}. "
+                        f"Loss value: {loss}. Terminating training immediately."
+                    )
+                else:
+                    io_utils.print_msg(
+                        f"Batch {batch}: Invalid loss, terminating training"
+                    )
+                    self.model.stop_training = True