diff --git a/qiskit/transpiler/preset_passmanagers/builtin_plugins.py b/qiskit/transpiler/preset_passmanagers/builtin_plugins.py
index 8c928a47f69..85b0c05d5ca 100644
--- a/qiskit/transpiler/preset_passmanagers/builtin_plugins.py
+++ b/qiskit/transpiler/preset_passmanagers/builtin_plugins.py
@@ -42,6 +42,7 @@
     CommutativeCancellation,
     ConsolidateBlocks,
     InverseCancellation,
+    RemoveIdentityEquivalent,
 )
 from qiskit.transpiler.passes import Depth, Size, FixedPoint, MinimumPoint
 from qiskit.transpiler.passes.utils.gates_basis import GatesInBasis
@@ -156,6 +157,13 @@ def pass_manager(self, pass_manager_config, optimization_level=None) -> PassMana
             if pass_manager_config.routing_method != "none":
                 init.append(ElidePermutations())
             init.append(RemoveDiagonalGatesBeforeMeasure())
+            # Target not set on RemoveIdentityEquivalent because we haven't applied a Layout
+            # yet so doing anything relative to an error rate in the target is not valid.
+            init.append(
+                RemoveIdentityEquivalent(
+                    approximation_degree=pass_manager_config.approximation_degree
+                )
+            )
             init.append(
                 InverseCancellation(
                     [
@@ -580,6 +588,10 @@ def _opt_control(property_set):
 
             elif optimization_level == 2:
                 _opt = [
+                    RemoveIdentityEquivalent(
+                        approximation_degree=pass_manager_config.approximation_degree,
+                        target=pass_manager_config.target,
+                    ),
                     Optimize1qGatesDecomposition(
                         basis=pass_manager_config.basis_gates, target=pass_manager_config.target
                     ),
@@ -602,6 +614,10 @@ def _opt_control(property_set):
                         plugin_config=pass_manager_config.unitary_synthesis_plugin_config,
                         target=pass_manager_config.target,
                     ),
+                    RemoveIdentityEquivalent(
+                        approximation_degree=pass_manager_config.approximation_degree,
+                        target=pass_manager_config.target,
+                    ),
                     Optimize1qGatesDecomposition(
                         basis=pass_manager_config.basis_gates, target=pass_manager_config.target
                     ),
diff --git a/releasenotes/notes/add-identity-pass-builtin-2061b29b53b928d3.yaml b/releasenotes/notes/add-identity-pass-builtin-2061b29b53b928d3.yaml
new file mode 100644
index 00000000000..0cf3d503aee
--- /dev/null
+++ b/releasenotes/notes/add-identity-pass-builtin-2061b29b53b928d3.yaml
@@ -0,0 +1,8 @@
+---
+features_transpiler:
+  - |
+    The :class:`.RemoveIdentityEquivalent` transpiler pass is now run as part
+    of the preset pass managers at optimization levels 2 and 3. The pass is
+    run in the ``init`` stage and the ``optimization`` stage, because the
+    optimizations it applies are valid in both stages and the pass is
+    fast to execute.
diff --git a/test/python/compiler/test_transpiler.py b/test/python/compiler/test_transpiler.py
index 851117671ef..851c6817d82 100644
--- a/test/python/compiler/test_transpiler.py
+++ b/test/python/compiler/test_transpiler.py
@@ -1796,21 +1796,29 @@ def test_no_infinite_loop(self, optimization_level):
             seed_transpiler=42,
         )
 
-        # Expect a -pi/2 global phase for the U3 to RZ/SX conversion, and
-        # a -0.5 * theta phase for RZ to P twice, once at theta, and once at 3 pi
-        # for the second and third RZ gates in the U3 decomposition.
-        expected = QuantumCircuit(
-            1, global_phase=-np.pi / 2 - 0.5 * (-0.2 + np.pi) - 0.5 * 3 * np.pi
-        )
-        expected.p(-np.pi, 0)
-        expected.sx(0)
-        expected.p(np.pi - 0.2, 0)
-        expected.sx(0)
+        if optimization_level == 1:
+            # Expect a -pi/2 global phase for the U3 to RZ/SX conversion, and
+            # a -0.5 * theta phase for RZ to P twice, once at theta, and once at 3 pi
+            # for the second and third RZ gates in the U3 decomposition.
+            expected = QuantumCircuit(
+                1, global_phase=-np.pi / 2 - 0.5 * (-0.2 + np.pi) - 0.5 * 3 * np.pi
+            )
+            expected.p(-np.pi, 0)
+            expected.sx(0)
+            expected.p(np.pi - 0.2, 0)
+            expected.sx(0)
+        else:
+            expected = QuantumCircuit(1, global_phase=(15 * np.pi - 1) / 10)
+            expected.sx(0)
+            expected.p(1.0 / 5.0 + np.pi, 0)
+            expected.sx(0)
+            expected.p(3 * np.pi, 0)
 
         error_message = (
             f"\nOutput circuit:\n{out!s}\n{Operator(out).data}\n"
             f"Expected circuit:\n{expected!s}\n{Operator(expected).data}"
         )
+        self.assertEqual(Operator(qc), Operator(out))
         self.assertEqual(out, expected, error_message)
 
     @data(0, 1, 2, 3)