diff --git a/tools/markdown_release_notes.py b/tools/markdown_release_notes.py
index 73bdbf775..cdae474f5 100644
--- a/tools/markdown_release_notes.py
+++ b/tools/markdown_release_notes.py
@@ -1,14 +1,53 @@
 #!/usr/bin/env python
 import re
 import sys
+from collections import defaultdict
+from functools import cache
+from operator import call
 from pathlib import Path
 
+from sphinx.ext.intersphinx import fetch_inventory
+
 CHANGELOG = Path(__file__).parent.parent / 'Changelog'
 
 # Match release lines like "5.2.0 (Monday 11 December 2023)"
 RELEASE_REGEX = re.compile(r"""((?:\d+)\.(?:\d+)\.(?:\d+)) \(\w+ \d{1,2} \w+ \d{4}\)$""")
 
 
+class MockConfig:
+    intersphinx_timeout: int | None = None
+    tls_verify = False
+    tls_cacerts: str | dict[str, str] | None = None
+    user_agent: str = ''
+
+
+@call
+class MockApp:
+    srcdir = ''
+    config = MockConfig()
+
+
+fetch_inv = cache(fetch_inventory)
+
+
+def get_intersphinx(obj):
+    module = obj.split('.', 1)[0]
+
+    registry = defaultdict(lambda: 'https://docs.python.org/3')
+    registry.update(
+        numpy='https://numpy.org/doc/stable',
+    )
+
+    base_url = registry[module]
+
+    inventory = fetch_inv(MockApp, '', f'{base_url}/objects.inv')
+    # Check py: first, then whatever
+    for objclass in sorted(inventory, key=lambda x: not x.startswith('py:')):
+        if obj in inventory[objclass]:
+            return f'{base_url}/{inventory[objclass][obj][2]}'
+    raise ValueError("Couldn't lookup {obj}")
+
+
 def main():
     version = sys.argv[1]
     output = sys.argv[2]
@@ -46,7 +85,7 @@ def main():
     release_notes = re.sub(r'\n +', ' ', release_notes)
 
     # Replace pr/<number> with #<number> for GitHub
-    release_notes = re.sub(r'\(pr/(\d+)\)', r'(#\1)', release_notes)
+    release_notes = re.sub(r'pr/(\d+)', r'#\1', release_notes)
 
     # Replace :mod:`package.X` with [package.X](...)
     release_notes = re.sub(
@@ -76,6 +115,14 @@ def main():
         r'[\3](https://nipy.org/nibabel/reference/\1.html#\1.\2.\3)',
         release_notes,
     )
+    # Replace :<any>:`<ref>` with intersphinx lookup
+    for ref in re.findall(r'(:[^:]*:`~?\w[\w.]+\w`)', release_notes):
+        objclass, tilde, module, obj = re.match(r':([^:]*):`(~?)([\w.]+)\.(\w+)`', ref).groups()
+        url = get_intersphinx(f'{module}.{obj}')
+        mdlink = f'[{"" if tilde else module}{obj}]({url})'
+        release_notes = release_notes.replace(ref, mdlink)
+    # Replace RST links with Markdown links
+    release_notes = re.sub(r'`([^<`]*) <([^>]*)>`_+', r'[\1](\2)', release_notes)
 
     def python_doc(match):
         module = match.group(1)
@@ -84,10 +131,9 @@ def python_doc(match):
 
     release_notes = re.sub(r':meth:`~([\w.]+)\.(\w+)`', python_doc, release_notes)
 
-    output.write('## Release notes\n\n')
-    output.write(release_notes)
-
-    output.close()
+    with output:
+        output.write('## Release notes\n\n')
+        output.write(release_notes)
 
 
 if __name__ == '__main__':