The proposal, made by the nation's bishops, puts President Walesa in a potentially awkward position.
The nominee, Jan Olszewski, has been clashing with President Walesa.
Parliament's lower house threw out all four amendments to the law introduced by the Senate on Thursday in line with President Walesa's wishes.
The rejection was a setback for President Walesa, who is trying to tighten a law he says will produce a weak Parliament.
President Walesa addressed a meeting of the Council of Europe in Strasbourg, France, this week.
The omission to invite President Walesa - and as a consequence, the heads of other nations - is highly controversial in Germany itself.
A poll conducted last September, just after President Walesa's veto, showed a slim majority favoring a loosening of the current restrictions.
The names were rumoured to include President Walesa.
A spokesperson for President Walesa said on June 4 that the files had been selective and that the material was "to a large degree fabricated".
President Walesa neither rejected nor accepted the American offer of a weak security partnership.