New York — Police Commissioner William J. Bratton on Tuesday issued a stern rebuke to his predecessor, Raymond W. Kelly, challenging him to substantiate his assertion that the New York Police Department’s official tally of major crime was unreliable, particularly shootings.

“Shame on him,” Bratton said. “Let him back up that accusation,” he added, noting that Kelly had not provided any details on why he believed the department was manipulating the statistics.

“If you’re going to make it, stand up, be a big man, and explain what you’re talking about,” Bratton added.

The comments by Bratton were a sudden and steep escalation in what has been, for the past two years, a tense if cordial relationship between the city’s most significant police leaders of the past quarter-century. Kelly served as commissioner for all 12 years of the Bloomberg administration after having first done so under Mayor David N. Dinkins; Bratton is in his second stint as commissioner as well, after two years in the job under Mayor Rudolph Giuliani.

In a radio interview recorded this month, Kelly suggested that there were “some issues” with the official statistics and said, without elaborating, that the Police Department had changed the way it counts shootings in the city since Bratton took over as commissioner in 2014 under Mayor Bill de Blasio.

“I think there is some redefinition going on as to what amounts to a shooting,” Kelly said when asked about crime numbers, which are expected to register a 2 percent drop this year in major crime. “I think you have to take a hard look at those numbers.”

Police officials have strongly disputed that claim, saying shootings are counted in the exact same way now as they were under Kelly.

Since making the comments in an interview with Gregory Floyd, the president of the local Teamsters union, Kelly has not responded to requests for comment or elaboration. Kelly could not immediately be reached for comment on Tuesday; the interview is set to air on WNYM-AM.

Bratton suggested that Kelly made his comments to draw attention to his book, “Vigilance: My Life Serving America and Protecting Its Empire City.” It came out in September.

“It’s amazing what comments you’ll make when selling a book,” Bratton said. “His comments were outrageous,” and, he added, “denigrate” the hard work of “my police officers.”

When a reporter tried to ask a follow-up question, Bratton interjected: “You don’t need any follow-up; I just laid the challenge” to him.

De Blasio, who stood silently by as Bratton spoke during a news conference on security preparations for the New Year’s Eve celebration in Times Square, was asked afterward what he made of the commissioner’s remarks.

“I think the commissioner spoke eloquently,” the mayor said, before moving on to the next question.

Michael M. Grynbaum contributed reporting.