As London Breed stood on the steps of San Francisco City Hall for her victory speech after clinching the mayor’s race, she delivered a clear appeal for civic unity.

“Whether you voted for me or not ... I’ll be your mayor, too,” Breed said, promising to “bring the Board of Supervisors together for the purpose of solving our most challenging problems.”

A week later, however, Breed’s decision to step down as board president well before becoming mayor is rankling supervisors from the city’s progressive wing. Some deride Breed’s call for conciliation as an empty gesture as they watch their chances of electing one of their own to the city’s No. 2 job slip away.

By resigning her presidential duties after the board finishes its regular business on Tuesday, Breed will all but ensure that her successor will come from among her fellow moderate supervisors. Supervisors Ahsha Safaí and Malia Cohen have been mentioned as possible contenders.

Board presidents make committee assignments, and those determine which supervisors will often be in the public eye and which will toil in obscurity. They also decide which legislation gets fast-tracked and which goes through a maze of hearings.

The 11-member board’s six moderates hold a majority — but only for the next few weeks. After Rafael Mandelman becomes District Eight supervisor, the board will have a progressive majority. Mandelman ousted moderate incumbent Jeff Sheehy in this month’s election and will be sworn in next month — too late to vote for the board’s next president, who serves a two-year term.

“I don’t think this is a great move. It feels a little bit gamey, but it’s her choice,” Mandelman said of Breed’s timing. “I’m a little disappointed. I would love to be able to vote on who the board president is in my first six months on the board. But I look forward to working with Mayor Breed. I’m going to work with her whatever she does around this.”

Supervisor Hillary Ronen, a progressive who has said she would like to be board president, said Breed was pulling “a cynical move” that disenfranchises the city’s progressives.

“I’m really disappointed that Rafael Mandelman and the rest of us aren’t going to get an opportunity to elect who we believe is the best person to run the Board of Supervisors,” Ronen said. “It sets the exact opposite tone that she said she was going to set, and it’s a shame.”

Breed said she wanted to step down as board president soon to spend more time on her transition before her expected July 11 swearing-in. But she had little political obligation to reach out to progressives after they removed her as acting mayor in January in favor of Mark Farrell.

“Mayor-elect Breed has made it clear that she wants to focus on her transition to her duties as mayor and she wants a seamless transition to a new board president,” said Andrea Bruss, a legislative aide for Breed. “She has made her intentions public, in advance, and crystal clear. It’s unclear exactly who, if anyone, has six votes at this point.”

Supervisor Aaron Peskin, who helped engineer the January vote that installed Farrell, said Breed is sending “a message of, ‘We don’t want to work together — we want to shut one group out.’ Is it legal? Yes. Is it democratic and inclusive? No. It’s politics.”

He added, “The bottom line is, if you have six votes, you win.” With Mandelman’s swearing-in, said Peskin, “the progressives have six votes, and we will use those votes for the benefit of the people of San Francisco.”

Dominic Fracassa is a San Francisco Chronicle staff writer. Email: dfracassa@sfchronicle.com Twitter: @dominicfracassa