The question came on a small index card, and had been preoccupying many in the auditorium: Were the rumors true that August Martin High School could be closed?

The answer from schools Chancellor Carmen Fariña left no room for doubt.

“First of all, I hate rumors and the answer is no, no, no,” Fariña said Monday night at the school in South Jamaica, Queens, generating applause from the 30 or so community members gathered in the school’s auditorium.

City officials have been eager to make an example of August Martin, once considered among the worst in the state, but which has received extra resources through the city’s “Renewal” turnaround program and has made steady progress. Mayor Bill de Blasio visited the building on the first day of school — and on Monday night, with Fariña by her side, Principal Rory Parnell touted the school’s progress, including a graduation rate that shot up to 63 percent last school year, a 24 percentage point increase.

“I’ve never worked with a team of teachers that works this hard,” Parnell said.

In promising that August Martin was safe from closure, Fariña got out in front of city and state officials who have said decisions about which struggling schools could be closed or face other consequences would come later this fall.

August Martin is one of 25 city schools in the state’s “Receivership” program, which requires bottom-ranked schools to make improvements or face possible takeover by an outside entity or closure. The schools were given one or two years to make gains — a deadline that passed at the end of the previous school year.

Monday’s meeting was required under the Receivership program. While Fariña indicated that August Martin had made sufficient progress, the state education department has not yet publicly said whether the city’s Receivership schools met their goals or will face more serious interventions.

On Tuesday, a state official said those decisions would be announced this fall. (Last year, the state identified just one city school for takeover, which resulted in an agreement to close the school and reopen a new one in its place.)

All of the city’s Receivership schools are also part of the mayor’s Renewal program, a separate initiative that infuses low-performing schools with extra funding and social services.

For his part, de Blasio has said the city is conducting its own review of Renewal schools, a process that will result in some school closures and is scheduled to be announced later this year. Fariña’s comments Monday evening suggest the city has already decided that some schools will avoid closure, though officials did not say whether they have made decisions about the 77 other schools in the program.

City education department officials said Tuesday they were confident that August Martin would hit its improvement targets.

“Last night I said loud and clear: While there’s always more work ahead, they will not be closed,” Fariña said in a statement, calling it a “school on the move.”

Several parents and officials made similarly optimistic statements at Monday’s hearing, where they lauded Principal Parnell’s leadership.

“I see a great change,” parent Catina Parker told the audience. “It’s not perfect, but it’s way better than how it was two years ago.”