diff --git a/parso/python/errors.py b/parso/python/errors.py
index af66d9f..d9183cb 100644
--- a/parso/python/errors.py
+++ b/parso/python/errors.py
@@ -713,13 +713,10 @@ class _FutureImportRule(SyntaxRule):
 
 @ErrorFinder.register_rule(type='star_expr')
 class _StarExprRule(SyntaxRule):
-    message = "starred assignment target must be in a list or tuple"
     message_iterable_unpacking = "iterable unpacking cannot be used in comprehension"
     message_assignment = "can use starred expression only as assignment target"
 
     def is_issue(self, node):
-        if node.parent.type not in _STAR_EXPR_PARENTS:
-            return True
         if node.parent.type == 'testlist_comp':
             # [*[] for a in [1]]
             if node.parent.children[1].type in _COMP_FOR_TYPES:
@@ -982,7 +979,7 @@ class _FStringRule(SyntaxRule):
 
 
 class _CheckAssignmentRule(SyntaxRule):
-    def _check_assignment(self, node, is_deletion=False, is_namedexpr=False):
+    def _check_assignment(self, node, is_deletion=False, is_namedexpr=False, is_aug_assign=False):
         error = None
         type_ = node.type
         if type_ == 'lambdef':
@@ -1024,9 +1021,9 @@ class _CheckAssignmentRule(SyntaxRule):
                         # This is not a comprehension, they were handled
                         # further above.
                         for child in second.children[::2]:
-                            self._check_assignment(child, is_deletion, is_namedexpr)
+                            self._check_assignment(child, is_deletion, is_namedexpr, is_aug_assign)
                     else:  # Everything handled, must be useless brackets.
-                        self._check_assignment(second, is_deletion, is_namedexpr)
+                        self._check_assignment(second, is_deletion, is_namedexpr, is_aug_assign)
         elif type_ == 'keyword':
             if node.value == "yield":
                 error = "yield expression"
@@ -1069,12 +1066,15 @@ class _CheckAssignmentRule(SyntaxRule):
                 error = "f-string expression"
         elif type_ in ('testlist_star_expr', 'exprlist', 'testlist'):
             for child in node.children[::2]:
-                self._check_assignment(child, is_deletion, is_namedexpr)
+                self._check_assignment(child, is_deletion, is_namedexpr, is_aug_assign)
         elif ('expr' in type_ and type_ != 'star_expr'  # is a substring
               or '_test' in type_
               or type_ in ('term', 'factor')):
             error = 'operator'
         elif type_ == "star_expr":
+            if not search_ancestor(node, *_STAR_EXPR_PARENTS) and not is_aug_assign:
+                self.add_issue(node, message="starred assignment target must be in a list or tuple")
+
             self._check_assignment(node.children[1])
 
         if error is not None:
@@ -1109,7 +1109,7 @@ class _ExprStmtRule(_CheckAssignmentRule):
 
         if self._normalizer.version <= (3, 8) or not is_aug_assign:
             for before_equal in node.children[:-2:2]:
-                self._check_assignment(before_equal)
+                self._check_assignment(before_equal, is_aug_assign=is_aug_assign)
 
         if is_aug_assign:
             target = _remove_parens(node.children[0])
diff --git a/test/test_python_errors.py b/test/test_python_errors.py
index 743cb25..0b45f11 100644
--- a/test/test_python_errors.py
+++ b/test/test_python_errors.py
@@ -391,3 +391,26 @@ def test_repeated_kwarg():
 )
 def test_unparenthesized_genexp(source, no_errors):
     assert bool(_get_error_list(source)) ^ no_errors
+
+@pytest.mark.parametrize(
+    ('source', 'no_errors'), [
+        ('*x = 2', False),
+        ('(*y) = 1', False),
+        ('((*z)) = 1', False),
+        ('a, *b = 1', True),
+        ('a, *b, c = 1', True),
+        ('a, (*b), c = 1', True),
+        ('a, ((*b)), c = 1', True),
+        ('a, (*b, c), d = 1', True),
+        ('[*(1,2,3)]', True),
+        ('{*(1,2,3)}', True),
+        ('[*(1,2,3),]', True),
+        ('[*(1,2,3), *(4,5,6)]', True),
+        ('[0, *(1,2,3)]', True),
+        ('{*(1,2,3),}', True),
+        ('{*(1,2,3), *(4,5,6)}', True),
+        ('{0, *(4,5,6)}', True)
+    ]
+)
+def test_starred_expr(source, no_errors):
+    assert bool(_get_error_list(source, version="3")) ^ no_errors