diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 917f0dcf..cecad877 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -189,7 +189,7 @@ jobs:
     strategy:
       matrix:
         testenv: [lowest, release]
-        python-version: ["3.8", "3.9", "3.10", "3.11", "3.12"]
+        python-version: ["3.8", "3.9", "3.10", "3.11", "3.12", "3.13"]
     steps:
       - uses: actions/checkout@v4
 
diff --git a/reana_client/api/client.py b/reana_client/api/client.py
index 8263feba..17e36af5 100644
--- a/reana_client/api/client.py
+++ b/reana_client/api/client.py
@@ -7,7 +7,6 @@
 # under the terms of the MIT License; see LICENSE file for more details.
 """REANA REST API client."""
 
-import cgi
 import json
 import logging
 import os
@@ -17,6 +16,7 @@
 
 import requests
 from bravado.exception import HTTPError
+from reana_client.api.utils import get_content_disposition_filename
 from reana_client.config import ERROR_MESSAGES
 from reana_client.errors import FileDeletionError, FileUploadError
 from reana_client.utils import is_regular_path, is_uuid_v4
@@ -500,9 +500,9 @@ def download_file(workflow, file_name, access_token):
             verify=False,
         )
         if "Content-Disposition" in http_response.headers:
-            content_disposition = http_response.headers.get("Content-Disposition")
-            value, params = cgi.parse_header(content_disposition)
-            file_name = params.get("filename", "downloaded_file")
+            file_name = get_content_disposition_filename(
+                http_response.headers.get("Content-Disposition")
+            )
 
         # A zip archive is downloaded if multiple files are requested
         multiple_files_zipped = (
diff --git a/reana_client/api/utils.py b/reana_client/api/utils.py
index e781ddcd..dc226058 100644
--- a/reana_client/api/utils.py
+++ b/reana_client/api/utils.py
@@ -1,12 +1,14 @@
 # -*- coding: utf-8 -*-
 #
 # This file is part of REANA.
-# Copyright (C) 2019, 2020, 2021 CERN.
+# Copyright (C) 2019, 2020, 2021, 2024 CERN.
 #
 # REANA is free software; you can redistribute it and/or modify it
 # under the terms of the MIT License; see LICENSE file for more details.
 """REANA client API utils."""
 
+from email.message import Message
+
 
 def get_path_from_operation_id(paths_dict, operation_id):
     """Find API path based on operation id."""
@@ -17,3 +19,17 @@ def get_path_from_operation_id(paths_dict, operation_id):
             if paths_dict[path][method]["operationId"] == operation_id:
                 return path
     return None
+
+
+def get_content_disposition_filename(content_disposition_header):
+    """Retrieve filename from a Content-Disposition like header.
+
+    Using email module instead of cgi.parse header due to https://peps.python.org/pep-0594/#cgi
+
+    Return a filename if found, otherwise a default string.
+    """
+    msg = Message()
+    msg["content-disposition"] = content_disposition_header
+    filename = msg.get_filename()
+
+    return filename if filename else "downloaded_file"
diff --git a/setup.py b/setup.py
index 37d7213f..256e00c9 100644
--- a/setup.py
+++ b/setup.py
@@ -93,6 +93,7 @@
         "Programming Language :: Python :: 3.10",
         "Programming Language :: Python :: 3.11",
         "Programming Language :: Python :: 3.12",
+        "Programming Language :: Python :: 3.13",
         "Programming Language :: Python :: Implementation :: CPython",
         "Programming Language :: Python",
         "Topic :: Internet :: WWW/HTTP :: Dynamic Content",
diff --git a/tests/test_api_utils.py b/tests/test_api_utils.py
new file mode 100644
index 00000000..04f6a43f
--- /dev/null
+++ b/tests/test_api_utils.py
@@ -0,0 +1,33 @@
+# -*- coding: utf-8 -*-
+#
+# This file is part of REANA.
+# Copyright (C) 2024 CERN.
+#
+# REANA is free software; you can redistribute it and/or modify it
+# under the terms of the MIT License; see LICENSE file for more details.
+
+"""REANA API utils tests."""
+
+import pytest
+
+from reana_client.api.utils import get_content_disposition_filename
+
+
+@pytest.mark.parametrize(
+    "content_disposition_header, expected_filename",
+    [
+        ("inline", "downloaded_file"),
+        ("attachment", "downloaded_file"),
+        ('attachment; filename="example.txt"', "example.txt"),
+        ("attachment; filename*=UTF-8''example.txt", "example.txt"),
+        ("attachment; filename=folder", "folder"),
+        ('attachment; filename="folder/*/example.txt"', "folder/*/example.txt"),
+    ],
+)
+def test_get_content_disposition_filename(
+    content_disposition_header, expected_filename
+):
+    assert (
+        get_content_disposition_filename(content_disposition_header)
+        == expected_filename
+    )
diff --git a/tox.ini b/tox.ini
index 7b2db7b5..5f07b341 100644
--- a/tox.ini
+++ b/tox.ini
@@ -11,6 +11,7 @@ envlist =
     py310
     py311
     py312
+    py313
 
 [testenv]
 deps =