diff --git a/rdflib/plugin.py b/rdflib/plugin.py
index f7b98c99f..f3c01f1dc 100644
--- a/rdflib/plugin.py
+++ b/rdflib/plugin.py
@@ -378,6 +378,12 @@ def plugins(
     "rdflib.plugins.parsers.notation3",
     "TurtleParser",
 )
+register(
+    "application/x-turtle",
+    Parser,
+    "rdflib.plugins.parsers.notation3",
+    "TurtleParser",
+)
 register(
     "turtle",
     Parser,
diff --git a/rdflib/plugins/stores/sparqlconnector.py b/rdflib/plugins/stores/sparqlconnector.py
index 3dc2158f7..569e6e7d7 100644
--- a/rdflib/plugins/stores/sparqlconnector.py
+++ b/rdflib/plugins/stores/sparqlconnector.py
@@ -10,6 +10,7 @@
 from urllib.request import Request, urlopen
 
 from rdflib.plugin import plugins
+from rdflib.plugins.sparql import prepareQuery
 from rdflib.query import Result, ResultParser
 from rdflib.term import BNode
 from rdflib.util import FORMAT_MIMETYPE_MAP, RESPONSE_TABLE_FORMAT_MIMETYPE_MAP
@@ -92,6 +93,11 @@ def query(
 
         headers = {"Accept": self.response_mime_types()}
 
+        # change Accept header to an RDF mime type in case of a construct query
+        qtype = self.__get_query_type__(query)
+        if qtype in ("ConstructQuery", "DescribeQuery"):
+            headers.update({"Accept": self.response_mime_types_rdf()})
+
         args = copy.deepcopy(self.kwargs)
 
         # merge params/headers dicts
@@ -205,5 +211,30 @@ def response_mime_types(self) -> str:
                 supported_formats.add(plugin.name)
         return ", ".join(supported_formats)
 
+    def response_mime_types_rdf(self) -> str:
+        """Construct a HTTP-Header Accept field to reflect the supported mime types for SPARQL construct/describe queries that return a graph.
+
+        If the return_format parameter is set, the mime types are restricted to these accordingly.
+        """
+        rdf_mimetype_map = [
+            mime for mlist in FORMAT_MIMETYPE_MAP.values() for mime in mlist
+        ]
+
+        # use the matched returnType if it matches one of the rdf mime types
+        if self.returnFormat in FORMAT_MIMETYPE_MAP:
+            return FORMAT_MIMETYPE_MAP[self.returnFormat][0]
+        else:
+            return ", ".join(rdf_mimetype_map)
+
+    def __get_query_type__(self, query: str) -> str | None:
+        try:
+            q = prepareQuery(query)
+            algebra = getattr(q, "algebra", None)
+            name = getattr(algebra, "name", None)
+            return name  # e.g. 'SelectQuery', 'ConstructQuery', 'DescribeQuery', 'AskQuery'
+        except Exception:
+            log.debug(f"cannot parse query: {query}")
+        return None
+
 
 __all__ = ["SPARQLConnector", "SPARQLConnectorException"]
diff --git a/test/test_store/test_store_sparqlstore_query.py b/test/test_store/test_store_sparqlstore_query.py
index d17823087..1f16831df 100644
--- a/test/test_store/test_store_sparqlstore_query.py
+++ b/test/test_store/test_store_sparqlstore_query.py
@@ -127,3 +127,52 @@ def test_query_construct_format(
     logging.debug("request = %s", request)
     logging.debug("request.headers = %s", request.headers.as_string())
     assert request.path_query["query"][0] == query
+
+
+def test_query_construct_accept_header(
+    function_httpmock: ServedBaseHTTPServerMock,
+) -> None:
+    """
+    Test that no SPARQL result media types are used for construct queries
+    """
+    graph = Graph(
+        "SPARQLStore",
+        identifier="http://example.com",
+        bind_namespaces="none",
+    )
+    url = f"{function_httpmock.url}/query"
+    graph.open(url)
+
+    function_httpmock.responses[MethodName.GET].extend(
+        [
+            MockHTTPResponse(
+                200,
+                "OK",
+                b"<> a <#test> .",
+                {"Content-Type": ["text/turtle"]},
+            )
+        ]
+        * 2  # two identical responses
+    )
+
+    # case 1: construct query
+
+    query_construct = "CONSTRUCT WHERE { ?s ?p ?o }"
+    graph.query(query_construct)
+
+    request_construct = function_httpmock.requests[MethodName.GET].pop()
+    accept_header_construct = request_construct.headers.get("Accept", "").lower()
+    # 'Accept' header must not include types for XML or JSON sparql results
+    assert "application/sparql-results" not in accept_header_construct
+    # 'Accept' header should be at least the default RDF/XML
+    assert "application/rdf+xml" in accept_header_construct
+
+    # case 2: select query
+
+    query_select = "SELECT * WHERE { ?s ?p ?o }"
+    graph.query(query_select)
+
+    request_select = function_httpmock.requests[MethodName.GET].pop()
+    accept_header_select = request_select.headers.get("Accept", "").lower()
+    # 'Accept' header should include types for XML or JSON sparql results
+    assert "application/sparql-results" in accept_header_select