diff --git a/Lib/string.py b/Lib/string.py
index b57c79b75e5..72a09f72898 100644
--- a/Lib/string.py
+++ b/Lib/string.py
@@ -169,7 +169,8 @@ class Formatter:
         self.check_unused_args(used_args, args, kwargs)
         return result
 
-    def _vformat(self, format_string, args, kwargs, used_args, recursion_depth):
+    def _vformat(self, format_string, args, kwargs, used_args, recursion_depth,
+                 auto_arg_index=0):
         if recursion_depth < 0:
             raise ValueError('Max string recursion exceeded')
         result = []
@@ -185,6 +186,23 @@ class Formatter:
                 # this is some markup, find the object and do
                 #  the formatting
 
+                # handle arg indexing when empty field_names are given.
+                if field_name == '':
+                    if auto_arg_index is False:
+                        raise ValueError('cannot switch from manual field '
+                                         'specification to automatic field '
+                                         'numbering')
+                    field_name = str(auto_arg_index)
+                    auto_arg_index += 1
+                elif field_name.isdigit():
+                    if auto_arg_index:
+                        raise ValueError('cannot switch from manual field '
+                                         'specification to automatic field '
+                                         'numbering')
+                    # disable auto arg incrementing, if it gets
+                    # used later on, then an exception will be raised
+                    auto_arg_index = False
+
                 # given the field_name, find the object it references
                 #  and the argument it came from
                 obj, arg_used = self.get_field(field_name, args, kwargs)
@@ -195,7 +213,8 @@ class Formatter:
 
                 # expand the format spec, if needed
                 format_spec = self._vformat(format_spec, args, kwargs,
-                                            used_args, recursion_depth-1)
+                                            used_args, recursion_depth-1,
+                                            auto_arg_index=auto_arg_index)
 
                 # format the object and append to the result
                 result.append(self.format_field(obj, format_spec))
diff --git a/Lib/test/test_string.py b/Lib/test/test_string.py
index c2bdfdb0b01..3e6507151e5 100644
--- a/Lib/test/test_string.py
+++ b/Lib/test/test_string.py
@@ -32,6 +32,23 @@ class ModuleTest(unittest.TestCase):
         self.assertEqual(fmt.format("foo{0}", "bar"), "foobar")
         self.assertEqual(fmt.format("foo{1}{0}-{1}", "bar", 6), "foo6bar-6")
 
+    def test_auto_numbering(self):
+        fmt = string.Formatter()
+        self.assertEqual(fmt.format('foo{}{}', 'bar', 6),
+                         'foo{}{}'.format('bar', 6))
+        self.assertEqual(fmt.format('foo{1}{num}{1}', None, 'bar', num=6),
+                         'foo{1}{num}{1}'.format(None, 'bar', num=6))
+        self.assertEqual(fmt.format('{:^{}}', 'bar', 6),
+                         '{:^{}}'.format('bar', 6))
+        self.assertEqual(fmt.format('{:^{pad}}{}', 'foo', 'bar', pad=6),
+                         '{:^{pad}}{}'.format('foo', 'bar', pad=6))
+
+        with self.assertRaises(ValueError):
+            fmt.format('foo{1}{}', 'bar', 6)
+
+        with self.assertRaises(ValueError):
+            fmt.format('foo{}{1}', 'bar', 6)
+
     def test_conversion_specifiers(self):
         fmt = string.Formatter()
         self.assertEqual(fmt.format("-{arg!r}-", arg='test'), "-'test'-")
diff --git a/Misc/NEWS b/Misc/NEWS
index 654a7a230e1..2fe06ed5b60 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -39,6 +39,10 @@ Core and Builtins
 
 - Issue #20480: Add ipaddress.reverse_pointer. Patch by Leon Weber.
 
+- Issue #13598: Modify string.Formatter to support auto-numbering of 
+  replacement fields. It now matches the behavior of str.format() in
+  this regard.
+
 Library
 -------