In recent months, they have spoken almost daily, particularly since Mr. Giuliani helped install William C. Thompson Jr., the Brooklyn representative, as board president.

Dr. Impellizzeri, the board's vice president and its Brooklyn representative, has long been a vocal opponent of the condom plan.

Mr. Thompson, the Brooklyn representative to the board, said he stood behind the Chancellor for practical reasons.

Irene Impellizerri, the Brooklyn representative, declined to comment on the proposal.

An amended resolution proposed by the Brooklyn representative to the panel, Martine G. Guerrier, failed by a vote of 10 to 3.

Mr. Giuliani appointed Ms. Segarra as one of his two members last month, along with Irene Impellizzeri, who has been the Brooklyn representative.

And over the weekend, the chancellor rejected a compromise proposal put forward by the Brooklyn representative, Martine G. Guerrier, losing her support.

In a 7-to-0 vote,, the board chose William C. Thompson Jr., a Manhattan investment banker and the board's Brooklyn representative, as the new president.

And William C. Thompson Jr., the Brooklyn representative who serves as the school board's president, says he opposes any school-voucher plan.

Mr. Montanti said he sought Mr. Biaggi's intervention because Brooklyn representatives in Congress had declined to help his company.