diff --git a/Lib/zipfile.py b/Lib/zipfile.py
index e31c93a9474..93171358e41 100644
--- a/Lib/zipfile.py
+++ b/Lib/zipfile.py
@@ -1101,11 +1101,12 @@ class ZipFile:
                 # set the modified flag so central directory gets written
                 # even if no files are added to the archive
                 self._didModify = True
+                self._start_disk = 0
                 try:
-                    self.start_dir = self._start_disk = self.fp.tell()
+                    self.start_dir = self.fp.tell()
                 except (AttributeError, OSError):
                     self.fp = _Tellable(self.fp)
-                    self.start_dir = self._start_disk = 0
+                    self.start_dir = 0
                     self._seekable = False
                 else:
                     # Some file-like objects can provide tell() but not seek()
diff --git a/Misc/NEWS b/Misc/NEWS
index 31fdde1d04f..516c3229582 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -208,6 +208,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #29094: Offsets in a ZIP file created with extern file object and modes
+  "w" and "x" now are relative to the start of the file.
+
 - Issue #29079: Prevent infinite loop in pathlib.resolve() on Windows
 
 - Issue #13051: Fixed recursion errors in large or resized