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Mr. Weiner’s vow to seek treatment and to work to repair his tattered reputation did little to ease the furor.

Republicans suggested that Mrs. Pelosi was not tough enough on Mr. Weiner. Michael Steel, a press aide to Mr. Boehner, said in an email that Mr. Weiner’s intention to seek a leave of absence “puts the focus” on Mrs. Pelosi.

House Majority Leader Eric Cantor, Virginia Republican, who has called for Mr. Weiner to resign, said if Mr. Weiner does not leave, Democrats should consider taking away his committee assignment.