Index: Doc/library/re.rst
===================================================================
--- Doc/library/re.rst	(revision 74191)
+++ Doc/library/re.rst	(working copy)
@@ -338,11 +338,12 @@
 
 ``\d``
    For Unicode (str) patterns:
-      Matches any Unicode digit (which includes ``[0-9]``, and also many
-      other digit characters). If the :const:`ASCII` flag is used only
-      ``[0-9]`` is matched (but the flag affects the entire regular
-      expression, so in such cases using an explicit ``[0-9]`` may be a
-      better choice).
+      Matches any Unicode decimal digit; more specifically, matches
+      any character in Unicode category [Nd] (Number, Decimal Digit).
+      This includes ``[0-9]``, and also many other digit characters.
+      If the :const:`ASCII` flag is used only ``[0-9]`` is matched
+      (but the flag affects the entire regular expression, so in such
+      cases using an explicit ``[0-9]`` may be a better choice).
    For 8-bit (bytes) patterns:
       Matches any decimal digit; this is equivalent to ``[0-9]``.
 
Index: Lib/test/test_re.py
===================================================================
--- Lib/test/test_re.py	(revision 74191)
+++ Lib/test/test_re.py	(working copy)
@@ -605,6 +605,27 @@
         self.assertEqual(next(iter).span(), (4, 4))
         self.assertRaises(StopIteration, next, iter)
 
+    def test_bug_6561(self):
+        # '\d' should match characters in Unicode category 'Nd'
+        # (Number, Decimal Digit), but not those in 'Nl' (Number,
+        # Letter) or 'No' (Number, Other).
+        decimal_digits = [
+            '\u0037', # '\N{DIGIT SEVEN}', category 'Nd'
+            '\u0e58', # '\N{THAI DIGIT SIX}', category 'Nd'
+            '\uff10', # '\N{FULLWIDTH DIGIT ZERO}', category 'Nd'
+            ]
+        for x in decimal_digits:
+            self.assertEqual(re.match('\d', x).group(0), x)
+
+        not_decimal_digits = [
+            '\u2165', # '\N{ROMAN NUMERAL SIX}', category 'Nl'
+            '\u3039', # '\N{HANGZHOU NUMERAL TWENTY}', category 'Nl'
+            '\u2082', # '\N{SUBSCRIPT TWO}', category 'No'
+            '\u32b4', # '\N{CIRCLED NUMBER THIRTY NINE}', category 'No'
+            ]
+        for x in not_decimal_digits:
+            self.assertEqual(re.match('\d', x), None)
+
     def test_empty_array(self):
         # SF buf 1647541
         import array
Index: Modules/_sre.c
===================================================================
--- Modules/_sre.c	(revision 74191)
+++ Modules/_sre.c	(working copy)
@@ -168,7 +168,7 @@
 
 #if defined(HAVE_UNICODE)
 
-#define SRE_UNI_IS_DIGIT(ch) Py_UNICODE_ISDIGIT((Py_UNICODE)(ch))
+#define SRE_UNI_IS_DIGIT(ch) Py_UNICODE_ISDECIMAL((Py_UNICODE)(ch))
 #define SRE_UNI_IS_SPACE(ch) Py_UNICODE_ISSPACE((Py_UNICODE)(ch))
 #define SRE_UNI_IS_LINEBREAK(ch) Py_UNICODE_ISLINEBREAK((Py_UNICODE)(ch))
 #define SRE_UNI_IS_ALNUM(ch) Py_UNICODE_ISALNUM((Py_UNICODE)(ch))