There was general agreement that any future federation should focus on political and legislative matters, while also serving to encourage individual unions to do more to organize workers.

The leaders of several breakaway unions have called for changing the name of the A.F.L.-C.I.O. because they had vowed never to return to the same federation.

But many A.F.L.-C.I.O. officials argue that it would be silly to alter the name of such a well-known organization and replace it with a name that few Americans are familiar with.

Labor officials said they did not discuss on Wednesday who would succeed John J. Sweeney, 74, who is scheduled to step down this year after heading the A.F.L.-C.I.O. for 13 years.

Richard Trumka, the federation’s secretary-treasurer and former president of the United Mine Workers, has been lobbying among union presidents to succeed Mr. Sweeney. But some union leaders, especially those in the rival labor federation, say they want a fresh voice leading organized labor.

The reorganizing proposals that unions president have floated in recent days include a rotating presidency for the A.F.L.-C.I.O. or its successor federation, with the presidents of individual unions serving two-year terms as head of the parent federation.

One A.F.L.-C.I.O. official described that plan this way: “The dukes want to replace the king.”

But many officials oppose a rotating presidency, saying the parent federation needs a strong, visible president who, by dint of serving for several years, is recognized by Congress and the news media as the undisputed voice for labor.