“We’ve looked at the basic question,” the mayor said of his administration, which has sought to reduce the number of people held on Rikers and improve conditions for those who are there. But, he said, it would cost “billions of dollars that right now we don’t have,” never mind the sizable “logistical issues.”

For a mayor who has at times reveled in they-say-it-can’t-be-done promises and programs, it was a moment to display the sort of political pragmatism that he has tried to underscore in recent speeches and in his budget presentation, which contained few big new initiatives.

“I want to be real with people,” Mr. de Blasio said at one point on Tuesday.

“My job is to level with the people of New York City,” he said later.

There are roughly 10,000 inmates in the city’s jail system, a vast majority of whom are housed on Rikers Island. Any plan to close the crumbling facilities, which have been the site of brutal episodes of violence and are now subject to federal oversight, would probably require Mr. de Blasio to embark on a yearslong political war fought in many pitched battles.

(Already the de Blasio administration has struggled in the much smaller task of moving 16- and 17-year-old inmates from Rikers Island. No suitable alternative has been found so far.)

The first battle would be in the court system, where officials would have to wring efficiencies out of the process to bring the Rikers population to a more manageable level. That effort, joined by Mr. de Blasio as well as Ms. Mark-Viverito and Mr. Lippman, has already begun and is focused on bail and summons reform. But the culture of criminal justice would also have to shift — among lawyers, judges and district attorneys — to ensure that fewer New Yorkers languish in city jails awaiting trial, experts said.

The move would require changing “the way the city’s criminal justice system operates,” said Michael P. Jacobson, a former city correction commissioner who has written on downsizing prisons. By some estimates, those changes, coupled with diversion programs, could cut the jail population in half. “At that point, our rate would be a European rate,” he said, speaking of the proportion of New Yorkers who are in jail.