In 2003, police officers in New York City issued 557,570 summonses for the lowest-level offenses, like drinking in public or riding a bike on the sidewalk. A decade later, in 2013, the annual total fell to 439,029, and it continued to drop last year.

But throughout those years, one measure remained relatively constant: More than a third of all summonses, year in and year out, resulted in arrest warrants for failure to appear in court, according to a report released on Monday by the John Jay College of Criminal Justice.

“Something is inherently wrong,” when nearly 40 percent of “generally law-abiding people” fail to show up to court after receiving a summons, the state’s chief judge, Jonathan Lippman, said at the breakfast gathering where the report was released. To address the problem, he said, some offenses currently handled by the criminal court system could be dealt with administratively, much like traffic offenses.

The findings come amid public debate over how the city and its police should handle low-level offenses at a time of diminishing street crime yet increasing tension over police tactics, especially in minority communities.

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Roughly 14 percent of summonses issued between 2003 and 2013 still had outstanding warrants open as of December, the report found, representing potentially hundreds of thousands of people who remained entangled in the criminal justice system because of minor violations from years before.

Reform advocates have pointed to the disproportionate number of black and Hispanic men who are given summonses or arrested on low-level offenses. A John Jay report last year found that the bulk of misdemeanor arrests in the city involved racial minorities.

But the new summons report provides no such racial breakdown because, since 2006, the courts stopped collecting racial data on those given summonses.

Mayor Bill de Blasio and Judge Lippman said this month that the city would soon amend the summons form to add information about the race of the person cited, and clearer instructions on when to go to court. The changes are aimed, in part, at reducing the number of warrants.

At the same time, the City Council speaker, Melissa Mark-Viverito, an East Harlem Democrat, and the police commissioner, William J. Bratton, have publicly differed in recent days over a proposal that would alter the legal framework for treating misdemeanor crimes and violations that are currently dealt with using a criminal summons.

The goal of the proposal, which Council officials said was still being worked out, is to keep those accused of the low-level offenses, most of whom are racial minorities, out of the criminal justice system.

“There is a recognition,” said Councilman Rory I. Lancman, a Queens Democrat and a proponent of the changes, “that the system is broken.”

In one version, the Council would change the law to make the most common minor offenses — including public urination, public alcohol consumption, riding a bike on the sidewalk and fare evasion — punishable by a civil summons. Top police officials have complained that doing so would tie the hands of officers, who, without the threat of an arrest, would be unable to compel violators to provide proper identification so the summons could be completed accurately.

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Mr. de Blasio, a Democrat, has resisted taking a firm position on the Council proposal. But last week he aligned himself with Mr. Bratton and a focus on so-called quality-of-life policing. “I want to emphasize my vision of quality-of-life policing and my vision related to the broken-windows strategy is the same as Commissioner Bratton’s,” the mayor said.

The Police Department is set to unveil its own study of enforcement of low-level offenses, covering the period since Mr. Bratton took over the department in 2014.

Mr. Bratton, for his part, has increasingly pointed to the lower number of arrests this year and spoken in recent weeks of a “peace dividend” being paid to New Yorkers in the form of less police action amid historically low levels of crime citywide.

But he said that police officers must retain the power to arrest people for low-level offenses. “If you lose those powers to arrest, that’s where Pandora’s box is opened and the 1970s, 1980s, have the potential to come roaring back again,” he said on Monday, adding that the department is in “very active discussions” with the Council.

As far back as 1977, city judges contemplated treating some minor offenses outside the criminal court system. “Much of that which is brought before the court belongs before an administrative tribunal,” Richard A. Brown wrote in a memo that year, when he was a supervising judge.

Mr. Brown, now the Queens district attorney, said in an interview on Monday that he “doesn’t see the downside” in pursuing that approach. “For those of us that remember the old traffic court, it has improved substantially since the creation of the administrative tribunals.”

The report found that one in five summonses ended up in a guilty plea or a finding of guilty. The rest were either dismissed by a judge or thrown out by the court, either because they did not contain necessary information, or because the basis for the charge was found to be lacking. (The defendant entered a plea of not guilty in an exceedingly small fraction of cases.)

Of the cases in which the person pleaded or was found guilty, nearly all resulted in fines, a figure that rose to 99 percent of cases in 2013 from 82 percent in 2003. (Summonses for public urination and public intoxication can be settled by pleading guilty by mail and sending in a fine, as little as $25.)

The city imposed fines totaling $7.3 million in 2003; that figure fell to $5.3 million in 2013. The report did not say how much of that had been collected.

The largest drop in summonses from 2003 to 2013 was seen in those given to teenagers, especially for disorderly conduct.