Looks like Supervisor London Breed is easing up on her criticism of San Francisco Fire Chief Joanne Hayes-White — just as the Board of Supervisors prepares to decide who should be its next president.

Breed has been a vocal critic of the fire chief’s handling of the agency’s troubled ambulance division, raising questions since the beginning of this year about ambulance response times and, just two months ago, calling for Hayes-White to step down. Mayor Ed Lee has repeatedly defended Hayes-White and, while he never publicly rebuked Breed, his administration was not pleased with her criticisms.

But as Breed’s name swirls around City Hall as a potential replacement for board president David Chiu — who will depart for the Assembly in Sacramento next month — she is backing off a resolution she authored. That resolution urged the Fire Commission — which has responsibility for hiring and firing the chief — “to very critically evaluate the current leadership of the Fire Department and carefully heed the messages of the department’s employee organizations in light of the ongoing emergency medical services crisis within the department.”

Those employee groups, of course, had been calling for Hayes-White’s head.

The resolution was scheduled to be hard by a Board of Supervisors committee Thursday, but Breed pulled it.

Why? In a written statement, her aide, Conor Johnston explained.

“Supervisor Breed is engaged in an ongoing, holistic process to improve emergency medical services in San Francisco,” Johnston stated. “We have made some great progress working with Mayor Lee and many others, and she has decided to hold off on this resolution in deference to that process.”

Is it about the board presidency? We’ll let you decide.