diff --git a/cirq-core/cirq/contrib/qasm_import/_parser.py b/cirq-core/cirq/contrib/qasm_import/_parser.py
index eeb6ec98dd3..3e13f011778 100644
--- a/cirq-core/cirq/contrib/qasm_import/_parser.py
+++ b/cirq-core/cirq/contrib/qasm_import/_parser.py
@@ -243,6 +243,24 @@ def __init__(self) -> None:
         'ch': QasmGateStatement(
             qasm_gate='ch', cirq_gate=ops.ControlledGate(ops.H), num_params=0, num_args=2
         ),
+        'cu1': QasmGateStatement(
+            qasm_gate='cu1',
+            num_params=1,
+            num_args=2,
+            cirq_gate=(lambda params: ops.ControlledGate(QasmUGate(0, 0, params[0] / np.pi))),
+        ),
+        'cu3': QasmGateStatement(
+            qasm_gate='cu3',
+            num_params=3,
+            num_args=2,
+            cirq_gate=(lambda params: ops.ControlledGate(QasmUGate(*[p / np.pi for p in params]))),
+        ),
+        'crz': QasmGateStatement(
+            qasm_gate='crz',
+            num_params=1,
+            num_args=2,
+            cirq_gate=(lambda params: ops.ControlledGate(ops.rz(params[0]))),
+        ),
         'swap': QasmGateStatement(qasm_gate='swap', cirq_gate=ops.SWAP, num_params=0, num_args=2),
         'cswap': QasmGateStatement(
             qasm_gate='cswap', num_params=0, num_args=3, cirq_gate=ops.CSWAP
diff --git a/cirq-core/cirq/contrib/qasm_import/_parser_test.py b/cirq-core/cirq/contrib/qasm_import/_parser_test.py
index 07c301a2add..3325bcd225a 100644
--- a/cirq-core/cirq/contrib/qasm_import/_parser_test.py
+++ b/cirq-core/cirq/contrib/qasm_import/_parser_test.py
@@ -924,16 +924,24 @@ def test_standard_gates_wrong_params_error(qasm_gate: str, num_params: int):
 ]
 
 
+# Mapping of two-qubit gates and `num_params`
+two_qubit_param_gates = {
+    ('cu1', cirq.ControlledGate(QasmUGate(0, 0, 0.1 / np.pi))): 1,
+    ('cu3', cirq.ControlledGate(QasmUGate(0.1 / np.pi, 0.2 / np.pi, 0.3 / np.pi))): 3,
+    ('crz', cirq.ControlledGate(cirq.rz(0.1))): 1,
+}
+
+
 @pytest.mark.parametrize('qasm_gate,cirq_gate', two_qubit_gates)
 def test_two_qubit_gates(qasm_gate: str, cirq_gate: cirq.testing.TwoQubitGate):
     qasm = f"""
-     OPENQASM 2.0;
-     include "qelib1.inc";
-     qreg q1[2];
-     qreg q2[2];
-     {qasm_gate} q1[0], q1[1];
-     {qasm_gate} q1, q2[0];
-     {qasm_gate} q2, q1;
+    OPENQASM 2.0;
+    include "qelib1.inc";
+    qreg q1[2];
+    qreg q2[2];
+    {qasm_gate} q1[0], q1[1];
+    {qasm_gate} q1, q2[0];
+    {qasm_gate} q2, q1;
 """
     parser = QasmParser()
 
@@ -961,11 +969,85 @@ def test_two_qubit_gates(qasm_gate: str, cirq_gate: cirq.testing.TwoQubitGate):
     assert parsed_qasm.qregs == {'q1': 2, 'q2': 2}
 
 
-@pytest.mark.parametrize('qasm_gate', [g[0] for g in two_qubit_gates])
+@pytest.mark.parametrize(
+    'qasm_gate,cirq_gate,num_params',
+    [
+        (gate_map[0], gate_map[1], num_param)
+        for gate_map, num_param in two_qubit_param_gates.items()
+    ],
+)
+def test_two_qubit_param_gates(
+    qasm_gate: str, cirq_gate: cirq.testing.TwoQubitGate, num_params: int
+):
+    params = '(0.1, 0.2, 0.3)' if num_params == 3 else '(0.1)'
+    qasm = f"""
+    OPENQASM 2.0;
+    include "qelib1.inc";
+    qreg q1[2];
+    qreg q2[2];
+    {qasm_gate}{params} q1[0], q1[1];
+    {qasm_gate}{params} q1, q2[0];
+    {qasm_gate}{params} q2, q1;
+    """
+    parser = QasmParser()
+
+    q1_0 = cirq.NamedQubit('q1_0')
+    q1_1 = cirq.NamedQubit('q1_1')
+    q2_0 = cirq.NamedQubit('q2_0')
+    q2_1 = cirq.NamedQubit('q2_1')
+
+    expected_circuit = cirq.Circuit()
+    expected_circuit.append(cirq_gate.on(q1_0, q1_1))
+    expected_circuit.append(cirq_gate.on(q1_0, q2_0))
+    expected_circuit.append(cirq_gate.on(q1_1, q2_0))
+    expected_circuit.append(cirq_gate.on(q2_0, q1_0))
+    expected_circuit.append(cirq_gate.on(q2_1, q1_1))
+    parsed_qasm = parser.parse(qasm)
+
+    assert parsed_qasm.supportedFormat
+    assert parsed_qasm.qelib1Include
+
+    ct.assert_same_circuits(parsed_qasm.circuit, expected_circuit)
+    assert parsed_qasm.qregs == {'q1': 2, 'q2': 2}
+
+
+@pytest.mark.parametrize(
+    'qasm_gate', [g[0] for g in two_qubit_gates] + [g[0] for g in two_qubit_param_gates.keys()]
+)
+def test_two_qubit_gates_not_enough_qubits(qasm_gate: str):
+    if qasm_gate in ('cu1', 'crz'):
+        qasm = f"""
+        OPENQASM 2.0;
+        include "qelib1.inc";
+        qreg q[2];
+        {qasm_gate}(0.1) q[0];
+    """
+    elif qasm_gate == 'cu3':
+        qasm = f"""
+        OPENQASM 2.0;
+        include "qelib1.inc";
+        qreg q[2];
+        {qasm_gate}(0.1, 0.2, 0.3) q[0];
+    """
+    else:
+        qasm = f"""
+        OPENQASM 2.0;
+        include "qelib1.inc";
+        qreg q[2];
+        {qasm_gate} q[0];
+    """
+
+    parser = QasmParser()
+
+    with pytest.raises(QasmException, match=rf".*{qasm_gate}.* takes 2 arg\(s\).*got.*1.*line 5"):
+        parser.parse(qasm)
+
+
+@pytest.mark.parametrize('qasm_gate', [g[0] for g in two_qubit_param_gates.keys()])
 def test_two_qubit_gates_not_enough_args(qasm_gate: str):
     qasm = f"""
-     OPENQASM 2.0;    
-     include "qelib1.inc";             
+     OPENQASM 2.0;
+     include "qelib1.inc";
      qreg q[2];
      {qasm_gate} q[0];
 """
@@ -976,19 +1058,27 @@ def test_two_qubit_gates_not_enough_args(qasm_gate: str):
         parser.parse(qasm)
 
 
-@pytest.mark.parametrize('qasm_gate', [g[0] for g in two_qubit_gates])
+@pytest.mark.parametrize(
+    'qasm_gate', [g[0] for g in two_qubit_gates] + [g[0] for g in two_qubit_param_gates.keys()]
+)
 def test_two_qubit_gates_with_too_much_parameters(qasm_gate: str):
+    if qasm_gate in ('cu1', 'cu3', 'crz'):
+        num_params_needed = 3 if qasm_gate == 'cu3' else 1
+    else:
+        num_params_needed = 0
+
     qasm = f"""
-     OPENQASM 2.0;    
-     include "qelib1.inc";             
-     qreg q[2];
-     {qasm_gate}(pi) q[0],q[1];
-"""
+        OPENQASM 2.0;
+        include "qelib1.inc";
+        qreg q[2];
+        {qasm_gate}(pi, pi/2, pi/3, pi/4) q[0],q[1];
+    """
 
     parser = QasmParser()
 
     with pytest.raises(
-        QasmException, match=rf".*{qasm_gate}.* takes 0 parameter\(s\).*got.*1.*line 5"
+        QasmException,
+        match=rf".*{qasm_gate}*. takes {num_params_needed} parameter\(s\).*got.*4.*line 5",
     ):
         parser.parse(qasm)
 
diff --git a/docs/build/interop.ipynb b/docs/build/interop.ipynb
index 26030a28c44..f38555e6fbd 100644
--- a/docs/build/interop.ipynb
+++ b/docs/build/interop.ipynb
@@ -315,9 +315,9 @@
     "|`swap`|`cirq.SWAP`|| \n",
     "|`ccx`|`cirq.CCX`|| \n",
     "|`cswap`|`cirq.CSWAP`|| \n",
-    "|`crz`| NOT supported || \n",
-    "|`cu1`| NOT supported|| \n",
-    "|`cu3`| NOT supported|| \n",
+    "|`crz`|`cirq.ControlledGate(cirq.Rz(θ))`|| \n",
+    "|`cu1`|`cirq.ControlledGate(u3(0,0,λ))`|| \n",
+    "|`cu3`|`cirq.ControlledGate(u3(θ,φ,λ))`|| \n",
     "|`rzz`| NOT supported|| "
    ]
   },