diff --git a/rest_framework/fields.py b/rest_framework/fields.py
index 2a08e09ff..16074b76a 100644
--- a/rest_framework/fields.py
+++ b/rest_framework/fields.py
@@ -1072,10 +1072,24 @@ class DateTimeField(Field):
             return value
 
         if output_format.lower() == ISO_8601:
+            if isinstance(value, str):
+                format_strings = (format_prefix + timezone_extension
+                                  for format_prefix in ('%Y-%m-%dT%H:%M', '%Y-%m-%dT%H:%M:%S', '%Y-%m-%dT%H:%M:%S.%f')
+                                  for timezone_extension in ('', '%Z', '%z'))
+                for format_string in format_strings:
+                    try:
+                        value = datetime.datetime.strptime(value, format_string)
+                        break
+                    except ValueError:
+                        pass
+                else:
+                    raise ValueError('DateTime String %s did not match any valid format string.' % value)
+
             value = value.isoformat()
             if value.endswith('+00:00'):
                 value = value[:-6] + 'Z'
             return value
+
         return value.strftime(output_format)
 
 
diff --git a/tests/test_fields.py b/tests/test_fields.py
index cefb45605..cce0181fa 100644
--- a/tests/test_fields.py
+++ b/tests/test_fields.py
@@ -978,6 +978,15 @@ class TestDateTimeField(FieldValues):
     outputs = {
         datetime.datetime(2001, 1, 1, 13, 00): '2001-01-01T13:00:00',
         datetime.datetime(2001, 1, 1, 13, 00, tzinfo=timezone.UTC()): '2001-01-01T13:00:00Z',
+        '2001-01-01T01:01': '2001-01-01T01:01:00',
+        '2001-01-01T01:01:01': '2001-01-01T01:01:01',
+        '2001-01-01T01:01:01.01': '2001-01-01T01:01:01.010000',
+        '2001-01-01T01:01+0100': '2001-01-01T01:01:00+01:00',
+        '2001-01-01T01:01:01+0100': '2001-01-01T01:01:01+01:00',
+        '2001-01-01T01:01:01.01+0100': '2001-01-01T01:01:01.010000+01:00',
+        '2001-01-01T01:01UTC': '2001-01-01T01:01:00',
+        '2001-01-01T01:01:01UTC': '2001-01-01T01:01:01',
+        '2001-01-01T01:01:01.01UTC': '2001-01-01T01:01:01.010000',
         None: None,
         '': None,
     }