diff --git a/qiskit/transpiler/passes/optimization/consolidate_blocks.py b/qiskit/transpiler/passes/optimization/consolidate_blocks.py
index 63dca11f6d2..ce64233699b 100644
--- a/qiskit/transpiler/passes/optimization/consolidate_blocks.py
+++ b/qiskit/transpiler/passes/optimization/consolidate_blocks.py
@@ -12,9 +12,11 @@
 
 """Replace each block of consecutive gates by a single Unitary node."""
 from __future__ import annotations
+from math import pi
 
 from qiskit.synthesis.two_qubit import TwoQubitBasisDecomposer
-from qiskit.circuit.library.standard_gates import CXGate, CZGate, iSwapGate, ECRGate
+from qiskit.circuit.library.standard_gates import CXGate, CZGate, iSwapGate, ECRGate, RXXGate
+
 from qiskit.transpiler.basepasses import TransformationPass
 from qiskit.transpiler.passmanager import PassManager
 from qiskit._accelerate.consolidate_blocks import consolidate_blocks
@@ -27,6 +29,7 @@
     "cz": CZGate(),
     "iswap": iSwapGate(),
     "ecr": ECRGate(),
+    "rxx": RXXGate(pi / 2),
 }
 
 
@@ -70,7 +73,6 @@ def __init__(
         if basis_gates is not None:
             self.basis_gates = set(basis_gates)
         self.force_consolidate = force_consolidate
-
         if kak_basis_gate is not None:
             self.decomposer = TwoQubitBasisDecomposer(kak_basis_gate)
         elif basis_gates is not None:
@@ -79,8 +81,12 @@ def __init__(
                 self.decomposer = TwoQubitBasisDecomposer(
                     KAK_GATE_NAMES[kak_gates.pop()], basis_fidelity=approximation_degree or 1.0
                 )
+            elif "rzx" in basis_gates:
+                self.decomposer = TwoQubitBasisDecomposer(
+                    CXGate(), basis_fidelity=approximation_degree or 1.0
+                )
             else:
-                self.decomposer = TwoQubitBasisDecomposer(CXGate())
+                self.decomposer = None
         else:
             self.decomposer = TwoQubitBasisDecomposer(CXGate())
 
diff --git a/test/python/transpiler/test_consolidate_blocks.py b/test/python/transpiler/test_consolidate_blocks.py
index 3b3aff1db22..fbe11ff77db 100644
--- a/test/python/transpiler/test_consolidate_blocks.py
+++ b/test/python/transpiler/test_consolidate_blocks.py
@@ -16,20 +16,19 @@
 
 import unittest
 import numpy as np
+from ddt import ddt, data
 
 from qiskit.circuit import QuantumCircuit, QuantumRegister, IfElseOp, Gate
 from qiskit.circuit.library import U2Gate, SwapGate, CXGate, CZGate, UnitaryGate
 from qiskit.converters import circuit_to_dag
-from qiskit.transpiler.passes import ConsolidateBlocks
 from qiskit.quantum_info.operators import Operator
 from qiskit.quantum_info.operators.measures import process_fidelity
-from qiskit.transpiler import PassManager
-from qiskit.transpiler import Target
-from qiskit.transpiler.passes import Collect1qRuns
-from qiskit.transpiler.passes import Collect2qBlocks
+from qiskit.transpiler import PassManager, Target, generate_preset_pass_manager
+from qiskit.transpiler.passes import ConsolidateBlocks, Collect1qRuns, Collect2qBlocks
 from test import QiskitTestCase  # pylint: disable=wrong-import-order
 
 
+@ddt
 class TestConsolidateBlocks(QiskitTestCase):
     """
     Tests to verify that consolidating blocks of gates into unitaries
@@ -571,6 +570,26 @@ def __init__(self):
 
         self.assertEqual(res, qc)
 
+    @data(2, 3)
+    def test_no_kak_gates_in_preset_pm(self, opt_level):
+        """Test correct initialization of ConsolidateBlocks pass when kak_gates aren't found.
+        Reproduces https://github.com/Qiskit/qiskit/issues/13438."""
+
+        qc = QuantumCircuit(2)
+        qc.cz(0, 1)
+        qc.sx([0, 1])
+        qc.cz(0, 1)
+
+        ref_pm = generate_preset_pass_manager(
+            optimization_level=1, basis_gates=["rz", "rzz", "sx", "x", "rx"]
+        )
+        ref_tqc = ref_pm.run(qc)
+        pm = generate_preset_pass_manager(
+            optimization_level=opt_level, basis_gates=["rz", "rzz", "sx", "x", "rx"]
+        )
+        tqc = pm.run(qc)
+        self.assertEqual(ref_tqc, tqc)
+
 
 if __name__ == "__main__":
     unittest.main()