The country's attorney general is considering filing charges against Olmert for allegedly double-billing Jewish groups for trips abroad. He wants Olmert to appear at a special hearing before making a final decision on whether to prosecute.
Olmert has already said that he will step down after elections scheduled in February. But Livni says he should go before that. His departure would clear the way for Livni to become acting prime minister until the election.
Livni was recently elected to succeed Olmert as leader of the ruling Kadima party.