diff --git a/monai/transforms/lazy/utils.py b/monai/transforms/lazy/utils.py
index 75f1e3529d0..0e9ff6f9716 100644
--- a/monai/transforms/lazy/utils.py
+++ b/monai/transforms/lazy/utils.py
@@ -192,6 +192,13 @@ def resample(data: torch.Tensor, matrix: NdarrayOrTensor, kwargs: dict | None =
     }
     ndim = len(matrix) - 1
     img = convert_to_tensor(data=data, track_meta=monai.data.get_track_meta())
+    if not (torch.is_floating_point(img) or torch.is_complex(img)):
+        warnings.warn(
+            f"Lazy resampling computes in floating point and converts the input of dtype {img.dtype} to "
+            "float32; the original data type is not preserved. For integer data such as label maps, set "
+            "`lazy=False` for the affected transforms (or cast back afterwards) if the data type must be preserved.",
+            stacklevel=2,
+        )
     init_affine = monai.data.to_affine_nd(ndim, img.affine)
     spatial_size = kwargs.get(LazyAttr.SHAPE, None)
     out_spatial_size = img.peek_pending_shape() if spatial_size is None else spatial_size
diff --git a/tests/transforms/functional/test_resample.py b/tests/transforms/functional/test_resample.py
index 40d264598d3..062a1b0b4de 100644
--- a/tests/transforms/functional/test_resample.py
+++ b/tests/transforms/functional/test_resample.py
@@ -12,6 +12,7 @@
 from __future__ import annotations
 
 import unittest
+import warnings
 
 import torch
 from parameterized import parameterized
@@ -45,6 +46,21 @@ def test_resample_function_impl(self, img, matrix, expected):
         out_1 = resample(img, matrix, {"lazy_resample_mode": "other value", "lazy_dtype": torch.float})
         self.assertIs(out.dtype, out_1.dtype)  # testing dtype in different lazy_resample_mode
 
+    def test_resample_warns_on_non_float_dtype(self):
+        """Lazy resampling upcasts non-floating-point inputs to float32; the user should be warned (see issue #6713)."""
+        img = convert_to_tensor(get_arange_img((3, 3)), dtype=torch.uint8)
+        with self.assertWarns(Warning):
+            out = resample(img, torch.eye(3), {"lazy_resample_mode": "auto"})
+        self.assertIs(out.dtype, torch.float32)
+        self.assertIs(img.dtype, torch.uint8)  # the input tensor itself is not mutated
+
+    def test_resample_no_warning_for_float_dtype(self):
+        """Float32 inputs do not trigger the lazy resampling dtype warning."""
+        img = convert_to_tensor(get_arange_img((3, 3)), dtype=torch.float32)
+        with warnings.catch_warnings():
+            warnings.simplefilter("error")  # turn any warning into an error
+            resample(img, torch.eye(3), {"lazy_resample_mode": "auto"})
+
 
 if __name__ == "__main__":
     unittest.main()