But unlike amnesty, Mr. Thompson said, his program forces people to take a measure of responsibility. They have to decide to deal with the issue: get up on a Saturday, visit a place teeming with the authorities and wait in line. Only then can they emerge with a clean record.

It is one front in a broader push for changes in the criminal justice system. From Baltimore to Ferguson, Mo., to Brooklyn, the scrutiny on law enforcement over the past year has given new light to longstanding inequities, and new energy to reform efforts.

In New York, the state’s chief judge, Jonathan Lippman, proposed overhauling a two-tiered bail system that keeps poor defendants in jail at Rikers Island and wealthier ones free. A new law in New York City prohibits employers from asking, on initial job applications, about a person’s criminal history.

By dealing with the warrants, Mr. Thompson said he thought he could help thousands of people — most black or Hispanic, and most of them young — eliminate crippling obstacles to finding work or housing, obtaining educational aid or even renting a car.

“This is the story of Ferguson,” said Alexander T. Tabarrok, a professor of economics at George Mason University who has studied the lessons of such programs, often called “Safe Surrender,” around the country. “The story of people who have become separated from the criminal justice system and are afraid of interacting with it.”

A Justice Department inquiry after the killing of Michael Brown in Ferguson described a place where many people saw small violations unnecessarily mushroom into far larger legal problems.