diff --git a/Lib/tarfile.py b/Lib/tarfile.py
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -179,7 +179,12 @@
             n = -(256 ** (len(s) - 1) - n)
     else:
         try:
-            n = int(nts(s, "ascii", "strict") or "0", 8)
+            u = nts(s, 'ascii', 'strict')
+            # Treat space as a terminating chaacter
+            u = u.lstrip(' ')
+            if ' ' in u:
+                u, _, _ = u.partition(' ')
+            n = int(u or "0", 8)
         except ValueError:
             raise InvalidHeaderError("invalid header")
     return n