diff --git a/Cython/Compiler/ParseTreeTransforms.py b/Cython/Compiler/ParseTreeTransforms.py
index 15feda18f018a3459b8970073d5c0af54f805854..60319f992f5a55fb135c10fc5bb0d053ed648b75 100644
--- a/Cython/Compiler/ParseTreeTransforms.py
+++ b/Cython/Compiler/ParseTreeTransforms.py
@@ -1190,6 +1190,7 @@ class ParallelRangeTransform(CythonTransform, SkipDeclarations):
     def visit_CallNode(self, node):
         self.visit(node.function)
         if not self.parallel_directive:
+            self.visitchildren(node, exclude=('function',))
             return node
 
         # We are a parallel directive, replace this node with the
diff --git a/tests/run/parallel.pyx b/tests/run/parallel.pyx
index c3526556f0f2d1905f4ed49e5d61c892333d699a..c3739b10bcebdbf831df4f0b616f21af47e6625c 100644
--- a/tests/run/parallel.pyx
+++ b/tests/run/parallel.pyx
@@ -8,6 +8,9 @@ from libc.stdlib cimport malloc, free
 
 openmp.omp_set_nested(1)
 
+cdef int forward(int x) nogil:
+    return x
+
 def test_parallel():
     """
     >>> test_parallel()
@@ -20,6 +23,9 @@ def test_parallel():
 
     with nogil, cython.parallel.parallel():
         buf[threadid()] = threadid()
+        # Recognise threadid() also when it's used in a function argument.
+        # See https://github.com/cython/cython/issues/3594
+        buf[forward(cython.parallel.threadid())] = forward(threadid())
 
     for i in range(maxthreads):
         assert buf[i] == i