diff --git a/build/pkgs/python3/spkg-configure.m4 b/build/pkgs/python3/spkg-configure.m4
index 78b4d8bda85..3dc3b7ea419 100644
--- a/build/pkgs/python3/spkg-configure.m4
+++ b/build/pkgs/python3/spkg-configure.m4
@@ -10,9 +10,9 @@ SAGE_SPKG_CONFIGURE([python3], [
         dnl Using Python 3 for Sage.  Check if we can do venv with a system python3
         dnl instead of building our own copy.
         check_modules="sqlite3, ctypes, math, hashlib, crypt, readline, socket, zlib, distutils.core"
-        AC_CACHE_CHECK([for python3 >= 3.7, < 3.9 with modules $check_modules], [ac_cv_path_PYTHON3], [
+        AC_CACHE_CHECK([for python3 > 3.6, < 3.9 with modules $check_modules], [ac_cv_path_PYTHON3], [
             AC_MSG_RESULT([])
-            AC_PATH_PROGS_FEATURE_CHECK([PYTHON3], [python3.8 python3.7 python3], [
+            AC_PATH_PROGS_FEATURE_CHECK([PYTHON3], [python3], [
                 AC_MSG_CHECKING([... whether $ac_path_PYTHON3 is good])
                 python3_version=`"$ac_path_PYTHON3" --version 2>&1 \
                     | $SED -n -e 's/\([[0-9]]*\.[[0-9]]*\.[[0-9]]*\).*/\1/p'`