diff --git a/Lib/test/test_int.py b/Lib/test/test_int.py
index db79926..09b9a77 100644
--- a/Lib/test/test_int.py
+++ b/Lib/test/test_int.py
@@ -233,16 +233,8 @@
         self.assertEqual(int(x=1.2), 1)
         self.assertEqual(int('100', base=2), 4)
         self.assertEqual(int(x='100', base=2), 4)
-
-    # For example, PyPy 1.9.0 raised TypeError for these cases because it
-    # expects x to be a string if base is given.
-    @support.cpython_only
-    def test_base_arg_with_no_x_arg(self):
-        self.assertEqual(int(base=6), 0)
-        # Even invalid bases don't raise an exception.
-        self.assertEqual(int(base=1), 0)
-        self.assertEqual(int(base=1000), 0)
-        self.assertEqual(int(base='foo'), 0)
+        self.assertRaises(TypeError, int, base=10)
+        self.assertRaises(TypeError, int, base=0)
 
     def test_int_base_limits(self):
         """Testing the supported limits of the int() base parameter."""
diff --git a/Misc/NEWS b/Misc/NEWS
index 334d439..e2a08dd 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -10,6 +10,9 @@
 Core and Builtins
 -----------------
 
+- Issue #16761: Calling ``int()`` with *base* argument only now raises
+  TypeError.
+
 - Issue #16759: Support the full DWORD (unsigned long) range in Reg2Py
   when retreiving a REG_DWORD value. This corrects functions like
   winreg.QueryValueEx that may have been returning truncated values.
diff --git a/Objects/longobject.c b/Objects/longobject.c
index 49e9d5d..5a50f24 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -4255,13 +4255,19 @@
     if (!PyArg_ParseTupleAndKeywords(args, kwds, "|OO:int", kwlist,
                                      &x, &obase))
         return NULL;
-    if (x == NULL)
+    if (x == NULL) {
+        if (obase != NULL) {
+            PyErr_SetString(PyExc_TypeError,
+                            "int() missing string argument");
+            return NULL;
+        }
         return PyLong_FromLong(0L);
+    }
     if (obase == NULL)
         return PyNumber_Long(x);
     if (!PyLong_Check(obase)) {
         PyErr_SetString(PyExc_TypeError,
-                        "int() arg 2 must be an integer.");
+                        "int() base must be an integer.");
         return NULL;
     }
 
@@ -4270,7 +4276,7 @@
         return NULL;
     if ((base != 0 && base < 2) || base > 36) {
         PyErr_SetString(PyExc_ValueError,
-                        "int() arg 2 must be >= 2 and <= 36");
+                        "int() base must be >= 2 and <= 36");
         return NULL;
     }