diff --git a/CHANGELOG.md b/CHANGELOG.md
index e289615ff..ea91ecce9 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,6 +10,16 @@ PLEASE REMEMBER TO CHANGE THE '..master' WITH AN ACTUAL TAG in GITHUB LINK.
 
 ## jax 0.2.14 (unreleased)
 * [GitHub commits](https://github.com/google/jax/compare/jax-v0.2.13...master).
+* New features:
+
+* Breaking changes:
+
+* Bug fixes:
+  * The {func}`jax2tf.convert` now scopes the `enable_xla` conversion parameter
+    properly to apply only during the just-in-time conversion
+    ({jax-issue}`#6720`).
+  * Fixed assertion failure in {func}`jax2tf.call_tf` when used with captured
+    `tf.Variable` ({jax-issue}`#6572`).
 
 * Bug fixes:
   * The {func}`jax2tf.convert` now converts `lax.dot_general` using the
diff --git a/jax/experimental/jax2tf/jax2tf.py b/jax/experimental/jax2tf/jax2tf.py
index 26af1fe2c..fafea2703 100644
--- a/jax/experimental/jax2tf/jax2tf.py
+++ b/jax/experimental/jax2tf/jax2tf.py
@@ -190,8 +190,6 @@ def convert(fun: Callable, *,
     A version of `fun` that expects TfVals as arguments (or
     tuple/lists/dicts) thereof, and returns TfVals as outputs.
   """
-  global _enable_xla
-  _enable_xla = enable_xla
   api._check_callable(fun)
 
   def converted_fun(*args: TfVal) -> TfVal:
@@ -276,6 +274,9 @@ def convert(fun: Callable, *,
     try:
       global _shape_env
       assert not _shape_env, f"Unexpected shape environment {_shape_env}"
+      global _enable_xla
+      prev_enable_xla = _enable_xla
+      _enable_xla = enable_xla
       _shape_env = shapeenv
 
       if with_gradient:
@@ -296,6 +297,7 @@ def convert(fun: Callable, *,
                     for o, _ in out_flat_raw]
     finally:
       _shape_env = {}
+      _enable_xla = prev_enable_xla
 
     out_flat = [tf.identity(x, "jax2tf_out") for x in out_flat]
     out = tree_util.tree_unflatten(out_tree_thunk(), out_flat)
diff --git a/jax/experimental/jax2tf/tests/jax2tf_test.py b/jax/experimental/jax2tf/tests/jax2tf_test.py
index 7b03afe55..e3d8cee59 100644
--- a/jax/experimental/jax2tf/tests/jax2tf_test.py
+++ b/jax/experimental/jax2tf/tests/jax2tf_test.py
@@ -22,6 +22,7 @@ from absl.testing import parameterized
 
 import jax
 from jax import dtypes
+from jax import lax
 from jax import numpy as jnp
 from jax import test_util as jtu
 from jax.config import config
@@ -516,6 +517,34 @@ class Jax2TfTest(tf_test_util.JaxToTfTestCase):
         tf_fn_array(np.array([3, 4, 5])), np.array([4.5, 10, 17.5],
                                                    jnp.bfloat16))
 
+  def test_enable_xla(self):
+    # Tests that enable_xla flag is properly scoped to a conversion.
+    def fun(x):
+      # Can be converted only if enable_xla is on, due to negative padding.
+      return lax.pad(x, np.float32(0), [(-1, 0, 0), (0, 0, 0)])
+
+    tf_fun_with_xla = jax2tf.convert(fun, enable_xla=True)
+    tf_fun_without_xla = jax2tf.convert(fun, enable_xla=False)
+    x = np.ones((2, 3), dtype=np.float32)
+
+    self.assertAllClose(fun(x), tf_fun_with_xla(x))
+    with self.assertRaisesRegex(NotImplementedError,
+                                "Call to pad cannot be converted with enable_xla=False"):
+      tf_fun_without_xla(x)
+
+    # Now in reverse order
+    def fun2(x):
+      # Can be converted only if enable_xla is on, due to negative padding.
+      return lax.pad(x, np.float32(0), [(-1, 0, 0), (0, 0, 0)])
+
+    tf_fun2_without_xla = jax2tf.convert(fun2, enable_xla=False)
+    tf_fun2_with_xla = jax2tf.convert(fun2, enable_xla=True)
+
+    with self.assertRaisesRegex(NotImplementedError,
+                                "Call to pad cannot be converted with enable_xla=False"):
+      tf_fun2_without_xla(x)
+    self.assertAllClose(fun(x), tf_fun2_with_xla(x))
+
 
 if __name__ == "__main__":
   absltest.main(testLoader=jtu.JaxTestLoader())