The expansion of program is an effort by the city, in the absence of sweeping reforms in Albany, to chip away at a bail system that officials, researchers and activists say amplifies inequities in the criminal justice system. Elizabeth Glazer, the director of the Mayor’s Office of Criminal Justice, said the Bail Expediting Program, which has been around since the 1980s, was an attractive way to reduce jail time for defendants “who shouldn’t have ended up there at all.”

“This issue of what do we do about people who are in for under a week has been a big focus” of the administration, Ms. Glazer said. “It’s the reason why we’re putting up an online bail system, we’re making sure there are cash machines in all the courthouses. All of these things that you would think, how important can they be, end up being quite important for someone to make bail as quickly as they can and from a courthouse.”

For its part, the City Council passed legislation in June increasing the length of the hold the Criminal Justice Agency can request from two hours up to 12 hours. Rory I. Lancman, one of sponsors of the bill, said it was necessary to help people work through a bail system that is “Kafkaesque.”

Critics say the changes focus on granular details and people charged with low-level, nonviolent offenses. Reform advocates say the city should also go after big-ticket reforms that help those charged with violent crimes, like Mr. Browder, who was charged with robbery.

Glenn E. Martin, the president and founder of JustLeadershipUSA, a nonprofit that aims to cut the nation’s prison population in half, said incremental changes were “Band-Aid fixes on a cancerous issue.”

“If you’re the mayor, you can afford to do big things,” he said.

Greg Berman, the director of the Center for Court Innovation, a nonprofit that documented the bail payment system in a 2015 report prepared for the mayor, said small changes were as necessary as big fixes. “There’s a lot you can do in the here and now,” he said.