diff --git a/swh/deposit/api/common.py b/swh/deposit/api/common.py
--- a/swh/deposit/api/common.py
+++ b/swh/deposit/api/common.py
@@ -853,8 +853,9 @@
             if headers.slug and metadata["atom:external_identifier"] != headers.slug:
                 raise DepositError(
                     BAD_REQUEST,
-                    "The 'external_identifier' tag is deprecated, "
-                    "the Slug header should be used instead.",
+                    "The <external_identifier> tag and Slug header are deprecated, "
+                    "<swh:create_origin> or <swh:add_to_origin> "
+                    "should be used instead.",
                 )
 
     def _empty_post(
diff --git a/swh/deposit/tests/api/test_collection_post_atom.py b/swh/deposit/tests/api/test_collection_post_atom.py
--- a/swh/deposit/tests/api/test_collection_post_atom.py
+++ b/swh/deposit/tests/api/test_collection_post_atom.py
@@ -261,7 +261,10 @@
         HTTP_SLUG="something",
     )
 
-    assert b"The &#39;external_identifier&#39; tag is deprecated" in response.content
+    assert (
+        b"The &lt;external_identifier&gt; tag and Slug header are deprecated"
+        in response.content
+    )
     assert response.status_code == status.HTTP_400_BAD_REQUEST