A clearer picture is expected to emerge this week, as Mr. de Blasio prepares for his first meeting with the city’s five district attorneys. A spokeswoman for the mayor, Marti Adams, declined to comment on the proposed policy change, although officials in two of the district attorney’s offices confirmed that the de Blasio administration was working on a new policy for how the police handle marijuana cases.

In an interview on Sunday, Mr. Thompson expressed concern about the mayor’s plan, calling it an end-run around the district attorneys that could end up hurting some of the very people the changes are supposed to help.

Since July, the Brooklyn district attorney’s office has dismissed 849 misdemeanor marijuana cases involving police arrests, or about 34 percent of the total 2,526 such cases in Brooklyn.

Under the proposed changes, it appears that instead of being arrested, those given a ticket for marijuana will be told to appear in a courtroom. But the new policy could push prosecutors out of the process, because summonses issued without an accompanying arrest generally do not receive prosecutorial review.

Image Police Commissioner William J. Bratton Credit... Michael Appleton for The New York Times

“In order to give the public confidence in the fairness of the criminal justice system, these cases should be subject to prosecutorial review,” Mr. Thompson said. “By allowing these cases to avoid early review, by issuing a summons, there is a serious concern that many summonses will be issued without the safeguards currently in place. These cases will move forward even when due process violations might have occurred.”

Another possible effect of the new policy would be that many of the tickets later convert into arrest warrants if the person misses a court date, he said. There are currently about 1.2 million active warrants in New York relating to missed court dates and unpaid fines for misdemeanors and noncriminal violations. In 2013, people failed to pay or show up to court about a quarter of the time for the 329,198 summons cases on the dockets of the city’s lowest level criminal courts, according to court statistics.