Federal prosecutors are seeking permission to retry Joseph L. Bruno, once the most powerful Republican in the state Legislature, after a U.S. Supreme Court ruling that they concede has invalidated Mr. Bruno’s conviction on two counts of depriving taxpayers of his honest services.

Richard S. Hartunian, U.S. attorney for the Northern District, in a 71-page brief filed Thursday, asked the U.S. Court of Appeals for the Second Circuit to vacate the December 2009 conviction but to grant permission to bring a superseding indictment on the two counts, the only charges for which Mr. Bruno was convicted.