The president of America’s national labor federation, the AFL-CIO, has won the support of a wavering union president by vowing to boost the labor movement’s outreach to the Republican Party.

The AFL-CIO’s president, John Sweeney, 71, who is up for re-election at a convention in Chicago next month, made the promise recently as he worked to beat back a challenge from dissenting unions that have charged Mr. Sweeney with moving too slowly to overhaul the labor federation.

The change in political strategy was disclosed yesterday by a labor leader who has long advocated a more bipartisan approach, Harold Schaitberger of the 250,000-member International Association of Fire Fighters.

“While the AFL-CIO will continue to support and maintain relationships with those Democrats who have historically and continuously supported the goals of our movement, it will also build bridges over party lines to Republicans who can be with us on selected issues,” Mr. Schaitberger said in a statement announcing his endorsement of Mr. Sweeney’s re-election bid.

A spokeswoman for Mr. Sweeney, Arlene Holt-Baker, confirmed the gist of the understanding but suggested it was not a significant departure from the AFL-CIO’s past practice.

“The wording, I think, is just a clarification that this is where the federation has always been. We’ll continue in our aggressive efforts to support politicians who support working families,” she said.

The meeting of the minds between Messrs. Sweeney and Schaitberger was somewhat unexpected, since the pair had a public and acrimonious falling out just a month ago. In a letter, Mr. Schaitberger accused the AFL-CIO boss of shutting him out of a major announcement on staffing changes at the federation. The firefighters’ chief called the episode “very telling” and said it fit a pattern of imperious leadership by Mr. Sweeney.

Shortly thereafter, Mr. Schaitberger convened a meeting of labor leaders who discussed easing Mr. Sweeney out of his post.

A spokesman for Mr. Schaitberger, Jeffrey Zack, said the two men patched up their differences in meetings over the past few weeks.

Last week, another union that wavered in its support for Mr. Sweeney, the United Auto Workers, said it would back the AFL-CIO chief’s re-election. The announcement signaled that dissident unions, like the Service Employees International Union, would not be able to win enough votes to oust Mr. Sweeney next month.

Mr. Zack said it was not fair to view Mr. Schaitberger’s move as a retreat in the face of the federation’s internal political realities.

“This isn’t just about votes,” Mr. Zack said.

A spokeswoman for the Service Employees declined to comment on the development. That union’s top leaders are scheduled to arrive in San Francisco today to discuss whether to withdraw from the AFL-CIO, a move that both proponents and opponents say would hurt the federation just as it is struggling to turn its fortunes around.