diff --git a/newsfragments/2914.changed.md b/newsfragments/2914.changed.md
new file mode 100644
index 00000000..bea926c4
--- /dev/null
+++ b/newsfragments/2914.changed.md
@@ -0,0 +1 @@
+FFI definition `PyIter_Check` on CPython 3.7 now does the equivalent for `hasattr(type(obj), "__next__")`, which works correctly on all platforms and adds support for `abi3`.
diff --git a/newsfragments/2914.fixed.md b/newsfragments/2914.fixed.md
new file mode 100644
index 00000000..9ea78ee8
--- /dev/null
+++ b/newsfragments/2914.fixed.md
@@ -0,0 +1 @@
+Fix downcast to `PyIterator` succeeding for Python classes which did not implement `__next__`.
diff --git a/pyo3-ffi/src/abstract_.rs b/pyo3-ffi/src/abstract_.rs
index b8306ca9..24ad4005 100644
--- a/pyo3-ffi/src/abstract_.rs
+++ b/pyo3-ffi/src/abstract_.rs
@@ -91,21 +91,22 @@ extern "C" {
     pub fn PyObject_GetIter(arg1: *mut PyObject) -> *mut PyObject;
 }
 
-// Defined as this macro in Python limited API, but relies on
-// non-limited PyTypeObject. Don't expose this since it cannot be used.
-#[cfg(not(any(Py_LIMITED_API, PyPy)))]
+// Before 3.8 PyIter_Check was defined in CPython as a macro,
+// but the implementation of that in PyO3 did not work, see
+// https://github.com/PyO3/pyo3/pull/2914
+//
+// This is a slow implementation which should function equivalently.
+#[cfg(not(any(Py_3_8, PyPy)))]
 #[inline]
 pub unsafe fn PyIter_Check(o: *mut PyObject) -> c_int {
-    (match (*crate::Py_TYPE(o)).tp_iternext {
-        Some(tp_iternext) => {
-            tp_iternext as *const std::os::raw::c_void != crate::_PyObject_NextNotImplemented as _
-        }
-        None => false,
-    }) as c_int
+    crate::PyObject_HasAttrString(
+        crate::Py_TYPE(o).cast(),
+        "__next__\0".as_ptr() as *const c_char,
+    )
 }
 
 extern "C" {
-    #[cfg(any(all(Py_3_8, Py_LIMITED_API), PyPy))]
+    #[cfg(any(Py_3_8, PyPy))]
     #[cfg_attr(PyPy, link_name = "PyPyIter_Check")]
     pub fn PyIter_Check(obj: *mut PyObject) -> c_int;
 
diff --git a/src/types/iterator.rs b/src/types/iterator.rs
index 5b51c067..cfbbd31b 100644
--- a/src/types/iterator.rs
+++ b/src/types/iterator.rs
@@ -3,7 +3,6 @@
 // based on Daniel Grunwald's https://github.com/dgrunwald/rust-cpython
 
 use crate::{ffi, AsPyPointer, IntoPyPointer, Py, PyAny, PyErr, PyNativeType, PyResult, Python};
-#[cfg(any(not(Py_LIMITED_API), Py_3_8))]
 use crate::{PyDowncastError, PyTryFrom};
 
 /// A Python iterator object.
@@ -29,7 +28,6 @@ use crate::{PyDowncastError, PyTryFrom};
 #[repr(transparent)]
 pub struct PyIterator(PyAny);
 pyobject_native_type_named!(PyIterator);
-#[cfg(any(not(Py_LIMITED_API), Py_3_8))]
 pyobject_native_type_extract!(PyIterator);
 
 impl PyIterator {
@@ -64,7 +62,6 @@ impl<'p> Iterator for &'p PyIterator {
 }
 
 // PyIter_Check does not exist in the limited API until 3.8
-#[cfg(any(not(Py_LIMITED_API), Py_3_8))]
 impl<'v> PyTryFrom<'v> for PyIterator {
     fn try_from<V: Into<&'v PyAny>>(value: V) -> Result<&'v PyIterator, PyDowncastError<'v>> {
         let value = value.into();
@@ -218,7 +215,7 @@ def fibonacci(target):
     }
 
     #[test]
-    #[cfg(any(not(Py_LIMITED_API), Py_3_8))]
+
     fn iterator_try_from() {
         Python::with_gil(|py| {
             let obj: Py<PyAny> = vec![10, 20].to_object(py).as_ref(py).iter().unwrap().into();
@@ -248,4 +245,76 @@ def fibonacci(target):
             assert_eq!(iter_ref.get_refcnt(), 2);
         })
     }
+
+    #[test]
+    #[cfg(feature = "macros")]
+    fn python_class_not_iterator() {
+        use crate::PyErr;
+
+        #[crate::pyclass(crate = "crate")]
+        struct Downcaster {
+            failed: Option<PyErr>,
+        }
+
+        #[crate::pymethods(crate = "crate")]
+        impl Downcaster {
+            fn downcast_iterator(&mut self, obj: &PyAny) {
+                self.failed = Some(obj.downcast::<PyIterator>().unwrap_err().into());
+            }
+        }
+
+        // Regression test for 2913
+        Python::with_gil(|py| {
+            let downcaster = Py::new(py, Downcaster { failed: None }).unwrap();
+            crate::py_run!(
+                py,
+                downcaster,
+                r#"
+                    from collections.abc import Sequence
+
+                    class MySequence(Sequence):
+                        def __init__(self):
+                            self._data = [1, 2, 3]
+
+                        def __getitem__(self, index):
+                            return self._data[index]
+
+                        def __len__(self):
+                            return len(self._data)
+
+                    downcaster.downcast_iterator(MySequence())
+                "#
+            );
+
+            assert_eq!(
+                downcaster.borrow_mut(py).failed.take().unwrap().to_string(),
+                "TypeError: 'MySequence' object cannot be converted to 'Iterator'"
+            );
+        });
+    }
+
+    #[test]
+    #[cfg(feature = "macros")]
+    fn python_class_iterator() {
+        #[crate::pyfunction(crate = "crate")]
+        fn assert_iterator(obj: &PyAny) {
+            assert!(obj.downcast::<PyIterator>().is_ok())
+        }
+
+        // Regression test for 2913
+        Python::with_gil(|py| {
+            let assert_iterator = crate::wrap_pyfunction!(assert_iterator, py).unwrap();
+            crate::py_run!(
+                py,
+                assert_iterator,
+                r#"
+                    class MyIter:
+                        def __next__(self):
+                            raise StopIteration
+
+                    assert_iterator(MyIter())
+                "#
+            );
+        });
+    }
 }