diff --git a/moto/sqs/models.py b/moto/sqs/models.py
index 044759e4f..9c8858bc0 100644
--- a/moto/sqs/models.py
+++ b/moto/sqs/models.py
@@ -38,6 +38,8 @@ class Message(BaseModel):
         self.sent_timestamp = None
         self.approximate_first_receive_timestamp = None
         self.approximate_receive_count = 0
+        self.deduplication_id = None
+        self.group_id = None
         self.visible_at = 0
         self.delayed_until = 0
 
@@ -400,7 +402,7 @@ class SQSBackend(BaseBackend):
         queue._set_attributes(attributes)
         return queue
 
-    def send_message(self, queue_name, message_body, message_attributes=None, delay_seconds=None):
+    def send_message(self, queue_name, message_body, message_attributes=None, delay_seconds=None, deduplication_id=None, group_id=None):
 
         queue = self.get_queue(queue_name)
 
@@ -412,6 +414,12 @@ class SQSBackend(BaseBackend):
         message_id = get_random_message_id()
         message = Message(message_id, message_body)
 
+        # Attributes, but not *message* attributes
+        if deduplication_id is not None:
+            message.deduplication_id = deduplication_id
+        if group_id is not None:
+            message.group_id = group_id
+
         if message_attributes:
             message.message_attributes = message_attributes
 
diff --git a/moto/sqs/responses.py b/moto/sqs/responses.py
index c475f0ce0..adf3e7a6e 100644
--- a/moto/sqs/responses.py
+++ b/moto/sqs/responses.py
@@ -198,6 +198,8 @@ class SQSResponse(BaseResponse):
     def send_message(self):
         message = self._get_param('MessageBody')
         delay_seconds = int(self._get_param('DelaySeconds', 0))
+        message_group_id = self._get_param("MessageGroupId")
+        message_dedupe_id = self._get_param("MessageDeduplicationId")
 
         if len(message) > MAXIMUM_MESSAGE_LENGTH:
             return ERROR_TOO_LONG_RESPONSE, dict(status=400)
@@ -213,7 +215,9 @@ class SQSResponse(BaseResponse):
             queue_name,
             message,
             message_attributes=message_attributes,
-            delay_seconds=delay_seconds
+            delay_seconds=delay_seconds,
+            deduplication_id=message_dedupe_id,
+            group_id=message_group_id
         )
         template = self.response_template(SEND_MESSAGE_RESPONSE)
         return template.render(message=message, message_attributes=message_attributes)
@@ -491,6 +495,18 @@ RECEIVE_MESSAGE_RESPONSE = """<ReceiveMessageResponse>
             <Name>ApproximateFirstReceiveTimestamp</Name>
             <Value>{{ message.approximate_first_receive_timestamp }}</Value>
           </Attribute>
+          {% if message.deduplication_id is not none %}
+          <Attribute>
+            <Name>MessageDeduplicationId</Name>
+            <Value>{{ message.deduplication_id }}</Value>
+          </Attribute>
+          {% endif %}
+          {% if message.group_id is not none %}
+          <Attribute>
+            <Name>MessageGroupId</Name>
+            <Value>{{ message.group_id }}</Value>
+          </Attribute>
+          {% endif %}
           {% if message.message_attributes.items()|count > 0 %}
           <MD5OfMessageAttributes>{{- message.attribute_md5 -}}</MD5OfMessageAttributes>
           {% endif %}
diff --git a/tests/test_sqs/test_sqs.py b/tests/test_sqs/test_sqs.py
index 05936ab39..c5ad39eb0 100644
--- a/tests/test_sqs/test_sqs.py
+++ b/tests/test_sqs/test_sqs.py
@@ -170,6 +170,28 @@ def test_message_with_complex_attributes():
     messages.should.have.length_of(1)
 
 
+@mock_sqs
+def test_send_message_with_message_group_id():
+    sqs = boto3.resource('sqs', region_name='us-east-1')
+    queue = sqs.create_queue(QueueName="test-group-id.fifo",
+                             Attributes={'FifoQueue': 'true'})
+
+    sent = queue.send_message(
+        MessageBody="mydata",
+        MessageDeduplicationId="dedupe_id_1",
+        MessageGroupId="group_id_1",
+    )
+
+    messages = queue.receive_messages()
+    messages.should.have.length_of(1)
+
+    message_attributes = messages[0].attributes
+    message_attributes.should.contain('MessageGroupId')
+    message_attributes['MessageGroupId'].should.equal('group_id_1')
+    message_attributes.should.contain('MessageDeduplicationId')
+    message_attributes['MessageDeduplicationId'].should.equal('dedupe_id_1')
+
+
 @mock_sqs
 def test_send_message_with_unicode_characters():
     body_one = 'Héllo!😀'