There were no arrests in three quarters of last year’s fatal shootings, according to statistics provided by Mr. Krasner’s office, even as arrests for illegal guns soared to record levels.

Only a small fraction of the people who are arrested for carrying guns without permits are the ones actually driving the violence, Mr. Krasner said. He insisted that the city needed to focus instead on people who had already proven themselves to be dangerous, and to invest in advanced forensic technology to clear the hundreds of unsolved shootings.

“What is their theory — that rather than go vigorously after the people who actually shoot the gun,” Mr. Krasner asked, “that we should take 100 people and put them in jail, because one of them might shoot somebody?”

Some city officials, including the police chief, see things differently.

“I think there are some philosophical differences between us,” said Police Commissioner Danielle M. Outlaw in an interview. She said she advocated “a both-and, not an either-or” approach. Earlier this year, the police created a special unit dedicated to investigating nonfatal shootings, with four dozen detectives and other officers working on cases across the city. But the commissioner insisted that the police were just as committed to cracking down on illegal gun possession as well.

“There have to be consequences for those who are carrying and using these guns illegally,” Ms. Outlaw said. “If I go out and get this gun, knowing nothing’s going to happen to me, why would that preclude me from doing anything else illegally with a gun?”

For those who live in the crisis every day, these questions are visceral.

Marguerite Ruff is a special education classroom assistant at an elementary school in Philadelphia. On a Saturday morning seven years ago, her youngest son, Justin, 23, was shot to death in the street.