On Tuesday, the union released a resolution adopted by its Executive Board that calls on Manchin to fill the seat.
Since Byrd's death at age 92 one week ago, there have been questions about who Manchin would appoint to fill the unexpired term and whether that appointee would face a special election. Byrd's term expires at noon on Jan. 3, 2013.
Manchin told The Associated Press last week that he wouldn't appoint himself. A Manchin spokeswoman didn't immediately return a telephone message Monday seeking comment on the AFL-CIO's resolution.