diff --git a/Include/pyport.h b/Include/pyport.h
index d30fcd7f6cb7da..abb526d503fddd 100644
--- a/Include/pyport.h
+++ b/Include/pyport.h
@@ -470,6 +470,14 @@ extern "C" {
 #  define WITH_THREAD
 #endif
 
+/* Some WebAssembly platforms do not provide a working pthread implementation.
+ * Thread support is stubbed and any attempt to create a new thread fails.
+ */
+#if (!defined(HAVE_PTHREAD_STUBS) && \
+      (!defined(__EMSCRIPTEN__) || defined(__EMSCRIPTEN_PTHREADS__)))
+#  define Py_CAN_START_THREADS 1
+#endif
+
 #ifdef WITH_THREAD
 #  ifdef Py_BUILD_CORE
 #    ifdef HAVE_THREAD_LOCAL
diff --git a/Modules/_testinternalcapi/test_critical_sections.c b/Modules/_testinternalcapi/test_critical_sections.c
index 238f29c3c62e64..9392096a16d1bf 100644
--- a/Modules/_testinternalcapi/test_critical_sections.c
+++ b/Modules/_testinternalcapi/test_critical_sections.c
@@ -170,6 +170,7 @@ thread_critical_sections(void *arg)
     }
 }
 
+#ifdef Py_CAN_START_THREADS
 static PyObject *
 test_critical_sections_threads(PyObject *self, PyObject *Py_UNUSED(args))
 {
@@ -194,12 +195,15 @@ test_critical_sections_threads(PyObject *self, PyObject *Py_UNUSED(args))
     Py_DECREF(test_data.obj1);
     Py_RETURN_NONE;
 }
+#endif
 
 static PyMethodDef test_methods[] = {
     {"test_critical_sections", test_critical_sections, METH_NOARGS},
     {"test_critical_sections_nest", test_critical_sections_nest, METH_NOARGS},
     {"test_critical_sections_suspend", test_critical_sections_suspend, METH_NOARGS},
+#ifdef Py_CAN_START_THREADS
     {"test_critical_sections_threads", test_critical_sections_threads, METH_NOARGS},
+#endif
     {NULL, NULL} /* sentinel */
 };