The opposition-controlled Senate on Wednesday vetoed a previous approval by the lower house, which still can override the veto. The nation's churches have had some property held by the state returned, and they are also to receive around $3 billion over 30 years.
The Communists have been vocal opponents of the payment. The lower house vote in January showed their rising influence. The party is not part of the center-left ruling coalition led by Prime Minister Andrej Babis, but helped the minority Cabinet survive a confidence vote.
The churches strictly oppose the taxation and plan to sue.